113 results
Search Results
2. Generalized split null point of sum of monotone operators in Hilbert spaces
- Author
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H. A. Abass, Olalwale K. Oyewole, Ojen Kumar Narain, Akindele Adebayo Mebawondu, and Kazeem Olalekan Aremu
- Subjects
47h09 ,Pure mathematics ,fixed point problem ,47j25 ,General Mathematics ,47j05 ,Hilbert space ,47h06 ,inertial iterative scheme ,symbols.namesake ,Monotone polygon ,firmly nonexpansive ,symbols ,generalized split monotone variational inclusion ,QA1-939 ,Null point ,Mathematics - Abstract
In this paper, we introduce a new type of a generalized split monotone variational inclusion (GSMVI) problem in the framework of real Hilbert spaces. By incorporating an inertial extrapolation method and an Halpern iterative technique, we establish a strong convergence result for approximating a solution of GSMVI and fixed point problems of certain nonlinear mappings in the framework of real Hilbert spaces. Many existing results are derived as corollaries to our main result. Furthermore, we present a numerical example to support our main result and propose an open problem for interested researchers in this area. The result obtained in this paper improves and generalizes many existing results in the literature.
- Published
- 2021
3. Further results on Ulam stability for a system of first-order nonsingular delay differential equations
- Author
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Jehad Alzabut, Bakhtawar Pervaiz, Akbar Zada, and Syed Omar Shah
- Subjects
010308 nuclear & particles physics ,General Mathematics ,02 engineering and technology ,Delay differential equation ,First order ,01 natural sciences ,Stability (probability) ,law.invention ,Invertible matrix ,law ,0103 physical sciences ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,020201 artificial intelligence & image processing ,Mathematics - Abstract
This paper is concerned with a system governed by nonsingular delay differential equations. We study the β-Ulam-type stability of the mentioned system. The investigations are carried out over compact and unbounded intervals. Before proceeding to the main results, we convert the system into an equivalent integral equation and then establish an existence theorem for the addressed system. To justify the application of the reported results, an example along with graphical representation is illustrated at the end of the paper.
- Published
- 2020
4. Equivalence of the existence of best proximity points and best proximity pairs for cyclic and noncyclic nonexpansive mappings
- Author
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Moosa Gabeleh and Hans-Peter A. Künzi
- Subjects
47h09 ,uniformly convex banach space ,lcsh:Mathematics ,General Mathematics ,010102 general mathematics ,best proximity (point) pair ,lcsh:QA1-939 ,01 natural sciences ,010101 applied mathematics ,Combinatorics ,46b20 ,0101 mathematics ,Equivalence (measure theory) ,noncyclic (cyclic) contraction ,Mathematics - Abstract
In this study, at first we prove that the existence of best proximity points for cyclic nonexpansive mappings is equivalent to the existence of best proximity pairs for noncyclic nonexpansive mappings in the setting of strictly convex Banach spaces by using the projection operator. In this way, we conclude that the main result of the paper [Proximal normal structure and nonexpansive mappings, Studia Math. 171 (2005), 283–293] immediately follows. We then discuss the convergence of best proximity pairs for noncyclic contractions by applying the convergence of iterative sequences for cyclic contractions and show that the convergence method of a recent paper [Convergence of Picard's iteration using projection algorithm for noncyclic contractions, Indag. Math. 30 (2019), no. 1, 227–239] is obtained exactly from Picard’s iteration sequence.
- Published
- 2020
5. 'An introduction to the edition of two Lemaître's original manuscripts'
- Author
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Dominique Lambert and Catherine de Maere
- Subjects
lcsh:Mathematics ,General Mathematics ,lcsh:QA1-939 ,15A66 ,Clifford algebras ,G.Lemaître ,Spinors ,01A70 ,Dirac equation ,Fermions ,Classics ,01A65 ,Mathematics ,Majorana - Abstract
The aim of this paper is to explain the contributions of G. Lemaître to Spinor Theory. At the end of the paper, we edited also, for the first time two short manuscripts: Spineurs et Quanta and Les spineurs et la physique quantique, written by Lemaître in December 1955 and in January 1956. This edition is a way of honouring Professor Michael Heller because he was the first, with Professor Odon Godart, who discovered, classified and published unedited manuscripts of G. Lemaître.
- Published
- 2017
6. Persistence and Global Attractivity for a Discretized Version of a General Model of Glucose-Insulin Interaction
- Author
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Dinh Cong Huong
- Subjects
Persistence (psychology) ,delay difference equations ,Discretization ,General Mathematics ,Insulin ,medicine.medical_treatment ,full time solution ,lcsh:Mathematics ,010102 general mathematics ,010103 numerical & computational mathematics ,lcsh:QA1-939 ,01 natural sciences ,non-standard difference ,medicine ,numerical discretized model ,Applied mathematics ,!-limit set of a persistent solution ,0101 mathematics ,Mathematics - Abstract
In this paper, we construct a non-standard finite difference scheme for a general model of glucose-insulin interaction. We establish some new sufficient conditions to ensure that the discretized model preserves the persistence and global attractivity of the continuous model. One of the main findings in this paper is that we derive two important propositions (Proposition 3.1 and Proposition 3.2) which are used to prove the global attractivity of the discretized model. Furthermore, when investigating the persistence and, in some cases, the global attractivity of the discretized model, the nonlinear functions f and h are not required to be differentiable. Hence, our results are more realistic because the statistical data of glucose and insulin are collected and reported in discrete time. We also present some numerical examples and their simulations to illustrate our results.
- Published
- 2016
7. Retracts of Ultrahomogeneous Structures in the Context of Katetov Functors
- Author
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Dragan Mašulović
- Subjects
Algebra ,Functor ,Katetov functors ,Fraïsse limits ,General Mathematics ,Retract ,lcsh:Mathematics ,Context (language use) ,retracts ,lcsh:QA1-939 ,Mathematics - Abstract
In this paper, we characterize retracts of a wide class of Fraïssé limits using the tools developed in a recent paper by W. Kubis and the present author, which we refer to as Katetov functors. This approach enables us to conclude that in many cases, a structure is a retract of a Fraïssé limit if and only if it is algebraically closed in the surrounding category.
- Published
- 2015
8. On an Open Problem of Xiao-Bin Zhang and Jun-Feng Xu
- Author
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S. Majumder
- Subjects
Discrete mathematics ,lcsh:Mathematics ,General Mathematics ,Open problem ,Zhàng ,uniqueness ,020206 networking & telecommunications ,010103 numerical & computational mathematics ,02 engineering and technology ,lcsh:QA1-939 ,01 natural sciences ,Bin ,nonlinear differential polynomials ,small functions ,0202 electrical engineering, electronic engineering, information engineering ,meromorphic function ,Uniqueness ,0101 mathematics ,Mathematics ,Meromorphic function - Abstract
The purpose of the paper is to study the uniqueness of meromorphic functions sharing a nonzero polynomial. The results of the paper improve and generalize the recent results due to X. B. Zhang and J. F. Xu [19]. We also solve an open problem as posed in the last section of [19].
- Published
- 2016
9. Relatively Orthocomplemented Skew Nearlattices in Rickart Rings
- Author
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Jānis Cīırulis
- Subjects
Discrete mathematics ,restrictive semigroup ,skew nearlattice ,lcsh:Mathematics ,General Mathematics ,Mathematics::Rings and Algebras ,Skew ,lcsh:QA1-939 ,right normal band ,right-star order ,relatively orthocomplemented poset ,Orthogonality ,orthogonality ,Rickart ring ,Mathematics - Abstract
A class of (right) Rickart rings, called strong, is isolated. In particular, every Rickart *-ring is strong. It is shown in the paper that every strong Rickart ring R admits a binary operation which turns R into a right normal band having an upper bound property with respect to its natural order ≤; such bands are known as right normal skew nearlattices. The poset (R, ≤) is relatively orthocomplemented; in particular, every initial segment in it is orthomodular.The order ≤ is actually a version of the so called right-star order. The one-sided star orders are well-investigated for matrices and recently have been generalized to bounded linear Hilbert space operators and to abstract Rickart *-rings. The paper demonstrates that they can successfully be treated also in Rickart rings without involution.
- Published
- 2015
10. Decay Rates of The Solution to the Cauchy Problem of the Type III Timoshenko Model Without Any Mechanical Damping
- Author
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Belkacem Said-Houari
- Subjects
decay rate ,lcsh:Mathematics ,General Mathematics ,Mathematical analysis ,Initial value problem ,heat conduction ,Type (model theory) ,lcsh:QA1-939 ,Thermal conduction ,type III heat conduction ,regularity loss ,Mathematics - Abstract
In this paper, we study the asymptotic behavior of the solutions of the one-dimensional Cauchy problem in Timoshenko system with thermal effect. The heat conduction is given by the type III theory of Green and Naghdi. We prove that the dissipation induced by the heat conduction alone is strong enough to stabilize the system, but with slow decay rate. To show our result, we transform our system into a first order system and, applying the energy method in the Fourier space, we establish some pointwise estimates of the Fourier image of the solution. Using those pointwise estimates, we prove the decay estimates of the solution and show that those decay estimates are very slow and, in the case of nonequal wave speeds, are of regularity-loss type. This paper solves the open problem stated in [10] and shows that the stability of the solution holds without any additional mechanical damping term.
- Published
- 2015
11. Certain Generalized q-Operators
- Author
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Prerna Maheshwari, Om Prakash, and Diwaker Sharma
- Subjects
Algebra ,q-Baskakov type operators ,Baskakov operator ,Rate of convergence ,weighted approximation ,q-integral operators ,lcsh:Mathematics ,General Mathematics ,Calculus ,Operator theory ,lcsh:QA1-939 ,rate of convergence ,Mathematics - Abstract
The applications of q-calculus in the approximation theory is a very interesting area of research in the recent years, several new q-operators were introduced and their behaviour were discussed by many researchers. This paper is the extension of the paper [15], in which Durrmeyer type generalization of q-Baskakov-Stancu type operators were discussed by using the concept of q-integral operators. Here, we propose to study the Stancu variant of q-Baskakov-Stancu type operators. We establish an estimate for the rate of convergence in terms of modulus of continuity and weighted approximation properties of these operators.
- Published
- 2015
12. L∞-error estimates of a finite element method for Hamilton-Jacobi-Bellman equations with nonlinear source terms with mixed boundary condition
- Author
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Madjda Miloudi, Samira Saadi, and Mohamed Haiour
- Subjects
47h09 ,algorithm ,General Mathematics ,fixed point hamilton-jacobi-bellman equation ,65m12 ,contraction ,finite element ,60h15 ,QA1-939 ,l∞-error estimate ,65f30 ,65l60 ,47h10 ,Mathematics - Abstract
In this paper, we introduce a new method to analyze the convergence of the standard finite element method for Hamilton-Jacobi-Bellman equation with noncoercive operators with nonlinear source terms with the mixed boundary conditions. The method consists of combining Bensoussan-Lions algorithm with the characterization of the solution, in both the continuous and discrete contexts, as fixed point of contraction. Optimal error estimates are then derived, first between the continuous algorithm and its finite element counterpart and then between the continuous solution and the approximate solution.
- Published
- 2021
13. Comparison of modified ADM and classical finite difference method for some third-order and fifth-order KdV equations
- Author
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Abey Sherif Kelil and Appanah Rao Appadu
- Subjects
35a22 ,General Mathematics ,modified adomian decomposition method ,Finite difference method ,classical finite difference method ,34a45 ,35a25 ,Third order ,Nonlinear Sciences::Exactly Solvable and Integrable Systems ,blow up ,QA1-939 ,Order (group theory) ,Applied mathematics ,Korteweg–de Vries equation ,nonlinear kdv equations ,Mathematics - Abstract
The KdV equation, which appears as an asymptotic model in physical systems ranging from water waves to plasma physics, has been studied. In this paper, we are concerned with dispersive nonlinear KdV equations by using two reliable methods: Shehu Adomian decomposition method (STADM) and the classical finite difference method for solving three numerical experiments. STADM is constructed by combining Shehu’s transform and Adomian decomposition method, and the nonlinear terms can be easily handled using Adomian’s polynomials. The Shehu transform is used to accelerate the convergence of the solution series in most cases and to overcome the deficiency that is mainly caused by unsatisfied conditions in other analytical techniques. We compare the approximate and numerical results with the exact solution for the two numerical experiments. The third numerical experiment does not have an exact solution and we compare profiles from the two methods vs the space domain at some values of time. This study provides us with information about which of the two methods are effective based on the numerical experiment chosen. Knowledge acquired will enable us to construct methods for other related partial differential equations such as stochastic Korteweg-de Vries (KdV), KdV-Burgers, and fractional KdV equations.
- Published
- 2021
14. Some results on generalized finite operators and range kernel orthogonality in Hilbert spaces
- Author
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Hadia Messaoudene, Asma Alharbi, and Nadia Mesbah
- Subjects
Pure mathematics ,General Mathematics ,Hilbert space ,numerical range ,class ℛ¯1 ,symbols.namesake ,Range (mathematics) ,Orthogonality ,47a12 ,orthogonality ,Kernel (statistics) ,symbols ,47a30 ,QA1-939 ,finite operator ,47b47 ,Mathematics - Abstract
Let ℋ {\mathcal{ {\mathcal H} }} be a complex Hilbert space and ℬ ( ℋ ) {\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }}) denotes the algebra of all bounded linear operators acting on ℋ {\mathcal{ {\mathcal H} }} . In this paper, we present some new pairs of generalized finite operators. More precisely, new pairs of operators ( A , B ) ∈ ℬ ( ℋ ) × ℬ ( ℋ ) \left(A,B)\in {\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }})\times {\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }}) satisfying: ∥ A X − X B − I ∥ ≥ 1 , for all X ∈ ℬ ( ℋ ) . \parallel AX-XB-I\parallel \ge 1,\hspace{1.0em}\hspace{0.1em}\text{for all}\hspace{0.1em}\hspace{0.33em}X\in {\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }}). An example under which the class of such operators is not invariant under similarity orbit is given. Range kernel orthogonality of generalized derivation is also studied.
- Published
- 2021
15. Range-Kernel orthogonality and elementary operators on certain Banach spaces
- Author
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Ahmed Bachir, Khalid Ouarghi, Abdelkader Segres, and Nawal Ali Sayyaf
- Subjects
trace class operators ,Pure mathematics ,schatten p-classes ,Nuclear operator ,General Mathematics ,Banach space ,47b10 ,Kernel (algebra) ,Range (mathematics) ,46b20 ,47b20 ,Orthogonality ,range-kernel orthogonality ,47a30 ,QA1-939 ,elementary operator ,47b47 ,Mathematics - Abstract
The characterization of the points in C p : 1 ≤ p < ∞ ( ℋ ) {C}_{p{:}_{1\le p\lt \infty }}\left({\mathcal{ {\mathcal H} }}) , the Von Neuman-Schatten p-classes, that are orthogonal to the range of elementary operators has been done for certain kinds of elementary operators. In this paper, we shall study this problem of characterization on an abstract reflexive, smooth and strictly convex Banach space for arbitrary operator. As an application, we consider other kinds of elementary operators defined on the spaces C p : 1 ≤ p < ∞ ( ℋ ) {C}_{p{:}_{1\le p\lt \infty }}\left({\mathcal{ {\mathcal H} }}) , and finally, we give a counterexample to Mecheri’s result given in this context.
- Published
- 2021
16. A statistical study of COVID-19 pandemic in Egypt
- Author
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Taha Radwan
- Subjects
2019-20 coronavirus outbreak ,Coronavirus disease 2019 (COVID-19) ,General Mathematics ,Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) ,coronavirus ,03 medical and health sciences ,0302 clinical medicine ,Order (exchange) ,62p10 ,0502 economics and business ,Pandemic ,QA1-939 ,62m10 ,65c20 ,030212 general & internal medicine ,Autoregressive integrated moving average ,Mathematics ,Actuarial science ,pandemic ,05 social sciences ,statistical model ,37m10 ,Linear relationship ,covid-19 ,time series analysis ,050211 marketing - Abstract
The spread of the COVID-19 started in Wuhan on December 31, 2019, and a powerful outbreak of the disease occurred there. According to the latest data, more than 165 million cases of COVID-19 infection have been detected in the world (last update May 19, 2021). In this paper, we propose a statistical study of COVID-19 pandemic in Egypt. This study will help us to understand and study the evolution of this pandemic. Moreover, documenting of accurate data and taken policies in Egypt can help other countries to deal with this epidemic, and it will also be useful in the event that other similar viruses emerge in the future. We will apply a widely used model in order to predict the number of COVID-19 cases in the coming period, which is the autoregressive integrated moving average (ARIMA) model. This model depicts the present behaviour of variables through linear relationship with their past values. The expected results will enable us to provide appropriate advice to decision-makers in Egypt on how to deal with this epidemic.
- Published
- 2021
17. Pythagorean harmonic summability of Fourier series
- Author
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Nassar H. S. Haidar
- Subjects
smoothing operator ,40g99 ,General Mathematics ,Harmonic mean ,Mathematics::Classical Analysis and ODEs ,pythagorean harmonic summability ,Harmonic (mathematics) ,01 natural sciences ,Mathematics::K-Theory and Homology ,FOS: Mathematics ,QA1-939 ,0101 mathematics ,Fourier series ,Mathematics ,Smoothing operator ,42a24 ,010102 general mathematics ,Pythagorean theorem ,Mathematical analysis ,40G99, 42A24, 42A99 ,Kalman filter ,semi-harmonic summability ,Functional Analysis (math.FA) ,Mathematics - Functional Analysis ,010101 applied mathematics ,42a99 ,single fourier series ,linear summability - Abstract
The paper explores the possibility for summing Fourier series nonlinearly via the Pythagorean harmonic mean. It reports on new results for this summability with introduction of new concepts like the smoothing operator and semi-harmonic summation. The smoothing operator is demonstrated to be Kalman filtering for linear summability, logistic processing for Pythagorean harmonic summability and linearized logistic processing for semi-harmonic summability. An emerging direct inapplicability of harmonic summability to seismic-like signals is shown to be resolvable by means of a regularizational asymptotic approach., Comment: 20 pages, 0 figures
- Published
- 2021
18. On some fixed point theorems for multivalued F-contractions in partial metric spaces
- Author
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Santosh Kumar and Sholastica Luambano
- Subjects
Pure mathematics ,General Mathematics ,partial metric spaces ,010102 general mathematics ,Fixed-point theorem ,Mathematics::General Topology ,01 natural sciences ,fixed point theorems ,010101 applied mathematics ,Metric space ,54h25 ,multivalued f-contraction mappings ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,QA1-939 ,0101 mathematics ,GeneralLiterature_REFERENCE(e.g.,dictionaries,encyclopedias,glossaries) ,47h10 ,Mathematics - Abstract
Altun et al. explored the existence of fixed points for multivalued F F -contractions and proved some fixed point theorems in complete metric spaces. This paper extended the results of Altun et al. in partial metric spaces and proved fixed point theorems for multivalued F F -contraction mappings. Some illustrative examples are provided to support our results. Moreover, an application for the existence of a solution of an integral equation is also enunciated, showing the materiality of the obtained results.
- Published
- 2021
19. On q-analogue of Janowski-type starlike functions with respect to symmetric points
- Author
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Bakhtiar Ahmad, Muhammad Zubair, Raees Khan, Muhammad Ghaffar Khan, and Zabidin Salleh
- Subjects
Pure mathematics ,starlike functions ,General Mathematics ,010102 general mathematics ,janowski functions ,02 engineering and technology ,30c45 ,Type (model theory) ,30c50 ,01 natural sciences ,0202 electrical engineering, electronic engineering, information engineering ,holomorphic functions ,QA1-939 ,020201 artificial intelligence & image processing ,0101 mathematics ,subordinations ,Mathematics - Abstract
The main objective of the present paper is to define a class of q q -starlike functions with respect to symmetric points in circular domain. Some interesting results of these functions have been evaluated in this article. The sufficiency criteria in the form of convolutions are evaluated. Furthermore, other geometric properties such as coefficient bounds, distortion theorem, closure theorem and extreme point theorem are also obtained for these newly defined functions.
- Published
- 2021
20. Solving two-dimensional nonlinear fuzzy Volterra integral equations by homotopy analysis method
- Author
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Atanaska Georgieva
- Subjects
convergence ,General Mathematics ,homotopy analysis method ,65r20 ,010103 numerical & computational mathematics ,02 engineering and technology ,01 natural sciences ,Fuzzy logic ,Volterra integral equation ,symbols.namesake ,Nonlinear system ,error estimation ,Convergence (routing) ,QA1-939 ,0202 electrical engineering, electronic engineering, information engineering ,symbols ,45g10 ,Applied mathematics ,two-dimensional nonlinear fuzzy volterra integral equation ,020201 artificial intelligence & image processing ,0101 mathematics ,41a25 ,Mathematics ,Homotopy analysis method - Abstract
The purpose of the paper is to find an approximate solution of the two-dimensional nonlinear fuzzy Volterra integral equation, as homotopy analysis method (HAM) is applied. Studied equation is converted to a nonlinear system of Volterra integral equations in a crisp case. Using HAM we find approximate solution of this system and hence obtain an approximation for the fuzzy solution of the nonlinear fuzzy Volterra integral equation. The convergence of the proposed method is proved. An error estimate between the exact and the approximate solution is found. The validity and applicability of the HAM are illustrated by a numerical example.
- Published
- 2021
21. More on μ-semi-Lindelöf sets in μ-spaces
- Author
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Mohammad S. Sarsak
- Subjects
Pure mathematics ,μ-semi-lindelöf space ,General Mathematics ,μ-space ,MathematicsofComputing_GENERAL ,54d20 ,54a10 ,μ-lindelöf set ,54a05 ,μ-semi-open ,μ-semi-lindelöf set ,generalized topology ,QA1-939 ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,μ-lindelöf space ,μ-open ,GeneralLiterature_REFERENCE(e.g.,dictionaries,encyclopedias,glossaries) ,Mathematics - Abstract
Sarsak [On μ \mu -compact sets in μ \mu -spaces, Questions Answers Gen. Topology 31 (2013), no. 1, 49–57] introduced and studied the class of μ \mu -Lindelöf sets in μ \mu -spaces. Mustafa [ μ \mu -semi compactness and μ \mu -semi Lindelöfness in generalized topological spaces, Int. J. Pure Appl. Math. 78 (2012), no. 4, 535–541] introduced and studied the class of μ \mu -semi-Lindelöf sets in generalized topological spaces (GTSs); the primary purpose of this paper is to investigate more properties and mapping properties of μ \mu -semi-Lindelöf sets in μ \mu -spaces. The class of μ \mu -semi-Lindelöf sets in μ \mu -spaces is a proper subclass of the class of μ \mu -Lindelöf sets in μ \mu -spaces. It is shown that the property of being μ \mu -semi-Lindelöf is not monotonic, that is, if ( X , μ ) \left(X,\mu ) is a μ \mu -space and A ⊂ B ⊂ X A\subset B\subset X , where A A is μ B {\mu }_{B} -semi-Lindelöf, then A A need not be μ \mu -semi-Lindelöf. We also introduce and study a new type of generalized open sets in GTSs, called ω μ {\omega }_{\mu } -semi-open sets, and investigate them to obtain new properties and characterizations of μ \mu -semi-Lindelöf sets in μ \mu -spaces.
- Published
- 2021
22. Inertial shrinking projection algorithm with self-adaptive step size for split generalized equilibrium and fixed point problems for a countable family of nonexpansive multivalued mappings
- Author
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Oluwatosin Temitope Mewomo, Abd-semii Oluwatosin-Enitan Owolabi, Musa A. Olona, and Timilehin Opeyemi Alakoya
- Subjects
Inertial frame of reference ,47j25 ,General Mathematics ,65j15 ,65k15 ,0211 other engineering and technologies ,Self adaptive ,step size ,firmly nonexpansive mapping ,02 engineering and technology ,90c33 ,Fixed point ,01 natural sciences ,QA1-939 ,nonexpansive multivalued mappings ,Applied mathematics ,Countable set ,fixed point problems ,0101 mathematics ,Dykstra's projection algorithm ,Mathematics ,021103 operations research ,inertial ,self-adaptive ,010101 applied mathematics ,split generalized equilibrium problems - Abstract
In this paper, we introduce a shrinking projection method of an inertial type with self-adaptive step size for finding a common element of the set of solutions of a split generalized equilibrium problem and the set of common fixed points of a countable family of nonexpansive multivalued mappings in real Hilbert spaces. The self-adaptive step size incorporated helps to overcome the difficulty of having to compute the operator norm, while the inertial term accelerates the rate of convergence of the proposed algorithm. Under standard and mild conditions, we prove a strong convergence theorem for the problems under consideration and obtain some consequent results. Finally, we apply our result to solve split mixed variational inequality and split minimization problems, and we present numerical examples to illustrate the efficiency of our algorithm in comparison with other existing algorithms. Our results complement and generalize several other results in this direction in the current literature.
- Published
- 2021
23. Dynamical study of Lyapunov exponents for Hide’s coupled dynamo model
- Author
-
Ali Allahem and Teflah Alresheedi
- Subjects
Chaotic flow ,lyapunov exponents ,General Mathematics ,regular flow ,02 engineering and technology ,Lyapunov exponent ,Dynamical system ,01 natural sciences ,dynamical system ,30c30 ,Physics::Fluid Dynamics ,symbols.namesake ,00a05 ,0103 physical sciences ,QA1-939 ,0202 electrical engineering, electronic engineering, information engineering ,chaotic flow ,11s82 ,010301 acoustics ,Mathematics ,15a06 ,Periodic flow ,Classical mechanics ,dynamo model ,15a60 ,symbols ,020201 artificial intelligence & image processing ,periodic flow ,Dynamo - Abstract
In this paper, we introduced the Lyapunov exponents (LEs) as a significant tool that is used to study the numerical solution behavior of the dynamical systems. Moreover, Hide’s coupled dynamo model presents a valuable dynamical study. We simulate the convergence of the LEs of the model in three cases by means of periodic flow, regular flow, and chaos flow. In addition, we compared these cases in logic connections and proved them in a mathematical way.
- Published
- 2021
24. A new iteration method for the solution of third-order BVP via Green's function
- Author
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Fatma Aydin Akgün and Zaur Rasulov
- Subjects
Iterative method ,General Mathematics ,47j05 ,integral operator ,green’s function ,fixed point iteration method ,symbols.namesake ,Third order ,boundary value problem ,Green's function ,QA1-939 ,symbols ,Applied mathematics ,47h10 ,Mathematics ,rate of convergence - Abstract
In this study, a new iterative method for third-order boundary value problems based on embedding Green’s function is introduced. The existence and uniqueness theorems are established, and necessary conditions are derived for convergence. The accuracy, efficiency and applicability of the results are demonstrated by comparing with the exact results and existing methods. The results of this paper extend and generalize the corresponding results in the literature.
- Published
- 2021
25. Numerical treatment of the generalized time-fractional Huxley-Burgers’ equation and its stability examination
- Author
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Faisal E. Abd Alaal, Adel R. Hadhoud, Ayman A. Abdelaziz, and Taha Radwan
- Subjects
65d07 ,General Mathematics ,the cubic b-spline ,stability analysis ,34dxx ,Stability (probability) ,Burgers' equation ,the generalized time-fractional huxley-burgers’ equation ,35r11 ,collocation method ,QA1-939 ,Applied mathematics ,65-xx ,the mean value theorem ,65l60 ,Mathematics - Abstract
In this paper, we show how to approximate the solution to the generalized time-fractional Huxley-Burgers’ equation by a numerical method based on the cubic B-spline collocation method and the mean value theorem for integrals. We use the mean value theorem for integrals to replace the time-fractional derivative with a suitable approximation. The approximate solution is constructed by the cubic B-spline. The stability of the proposed method is discussed by applying the von Neumann technique. The proposed method is shown to be conditionally stable. Several numerical examples are introduced to show the efficiency and accuracy of the method.
- Published
- 2021
26. Solving system of linear equations via bicomplex valued metric space
- Author
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Gnanaprakasam Arul Joseph, Boulaaras Salah Mahmoud, Mani Gunaseelan, Cherif Bahri, and Idris Sahar Ahmed
- Subjects
54h25 ,General Mathematics ,bicomplex valued metric space ,common fixed point linear equation ,46n99 ,47h9 ,30g35 ,QA1-939 ,47h10 ,Mathematics - Abstract
In this paper, we prove some common fixed point theorems on bicomplex metric space. Our results generalize and expand some of the literature’s well-known results. We also explore some of the applications of our key results.
- Published
- 2021
27. An iterative approximation of common solutions of split generalized vector mixed equilibrium problem and some certain optimization problems
- Author
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Olawale Kazeem Oyewole and Oluwatosin Temitope Mewomo
- Subjects
47h09 ,Optimization problem ,General Mathematics ,vector equilibrium problem ,47h06 ,46n10 ,split feasibility problem ,quasi-monotone mapping ,strong convergence ,QA1-939 ,Applied mathematics ,Iterative approximation ,Equilibrium problem ,generalized mixed equilibrium problem ,banach space ,Mathematics - Abstract
In this paper, we study the problem of finding a common solution of split generalized vector mixed equlibrium problem (SGVMEP), fixed point problem (FPP) and variational inequality problem (VIP). We propose an inertial-type iterative algorithm, which uses a projection onto a feasible set and a linesearch, which can be easily calculated. We prove a strong convergence of the sequence generated by the proposed algorithm to a common solution of SGVMEP, fixed point of a quasi- ϕ \phi -nonexpansive mapping and VIP for a general class of monotone mapping in 2-uniformly convex and uniformly smooth Banach space E 1 {E}_{1} and a smooth, strictly convex and reflexive Banach space E 2 {E}_{2} . Some numerical examples are presented to illustrate the performance of our method. Our result improves some existing results in the literature.
- Published
- 2021
28. On gradedJgr-classical 2-absorbing submodules of graded modules over graded commutative rings
- Author
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Khaldoun Al-Zoubi and Shatha Alghueiri
- Subjects
graded 2-absorbing submodule ,13a02 ,graded jgr -classical 2-absorbing submodule ,010201 computation theory & mathematics ,General Mathematics ,010102 general mathematics ,QA1-939 ,0102 computer and information sciences ,0101 mathematics ,01 natural sciences ,16w50 ,Mathematics ,graded classical 2-absorbing submodule - Abstract
LetGbe an abelian group with identityee. LetRbe aG-graded commutative ring with identity 1, andMMbe a gradedR-module. In this paper, we introduce the concept of gradedJgr{J}_{gr}-classical 2-absorbing submodule as a generalization of a graded classical 2-absorbing submodule. We give some results concerning of these classes of graded submodules. A proper graded submoduleCCofMMis called a gradedJgr{J}_{gr}-classical 2-absorbing submodule ofMM, if wheneverrg,sh,ti∈h(R){r}_{g},{s}_{h},{t}_{i}\in h\left(R)andxj∈h(M){x}_{j}\in h\left(M)withrgshtixj∈C{r}_{g}{s}_{h}{t}_{i}{x}_{j}\in C, then eitherrgshxj∈C+Jgr(M){r}_{g}{s}_{h}{x}_{j}\in C+{J}_{gr}\left(M)orrgtixj∈C+Jgr(M){r}_{g}{t}_{i}{x}_{j}\in C+{J}_{gr}\left(M)orshtixj∈C+Jgr(M),{s}_{h}{t}_{i}{x}_{j}\in C+{J}_{gr}\left(M),whereJgr(M){J}_{gr}\left(M)is the graded Jacobson radical.
- Published
- 2021
29. Two strongly convergent self-adaptive iterative schemes for solving pseudo-monotone equilibrium problems with applications
- Author
-
Nuttapol Pakkaranang, Habib ur Rehman, and Wiyada Kumam
- Subjects
47h09 ,fixed point problem ,47j25 ,General Mathematics ,47j05 ,47h06 ,pseudomonotone bifunction ,Self adaptive ,variational inequality problems ,strong convergence ,Monotone polygon ,Fixed point problem ,QA1-939 ,lipschitz-type conditions ,Applied mathematics ,Equilibrium problem ,equilibrium problem ,Mathematics - Abstract
The aim of this paper is to propose two new modified extragradient methods to solve the pseudo-monotone equilibrium problem in a real Hilbert space with the Lipschitz-type condition. The iterative schemes use a new step size rule that is updated on each iteration based on the value of previous iterations. By using mild conditions on a bi-function, two strong convergence theorems are established. The applications of proposed results are studied to solve variational inequalities and fixed point problems in the setting of real Hilbert spaces. Many numerical experiments have been provided in order to show the algorithmic performance of the proposed methods and compare them with the existing ones.
- Published
- 2021
30. Strong convergence inertial projection algorithm with self-adaptive step size rule for pseudomonotone variational inequalities in Hilbert spaces
- Author
-
Nuttapol Pakkaranang, Nopparat Wairojjana, and Nattawut Pholasa
- Subjects
Inertial frame of reference ,47h05 ,General Mathematics ,pseudomonotone mapping ,65k15 ,0211 other engineering and technologies ,Self adaptive ,010103 numerical & computational mathematics ,02 engineering and technology ,01 natural sciences ,lipschitz continuity ,symbols.namesake ,Convergence (routing) ,QA1-939 ,strong convergence theorem ,Applied mathematics ,0101 mathematics ,47h10 ,Dykstra's projection algorithm ,Mathematics ,021103 operations research ,Hilbert space ,68w10 ,extragradient-like algorithm ,Variational inequality ,65y05 ,symbols ,variational inequalities - Abstract
In this paper, we introduce a new algorithm for solving pseudomonotone variational inequalities with a Lipschitz-type condition in a real Hilbert space. The algorithm is constructed around two algorithms: the subgradient extragradient algorithm and the inertial algorithm. The proposed algorithm uses a new step size rule based on local operator information rather than its Lipschitz constant or any other line search scheme and functions without any knowledge of the Lipschitz constant of an operator. The strong convergence of the algorithm is provided. To determine the computational performance of our algorithm, some numerical results are presented.
- Published
- 2021
31. Applications of some operators on supra topological spaces
- Author
-
Tareq M. Al-shami, Baravan A. Asaad, and E. A. Abo-Tabl
- Subjects
Pure mathematics ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,General Mathematics ,010102 general mathematics ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,02 engineering and technology ,0101 mathematics ,Topological space ,GeneralLiterature_REFERENCE(e.g.,dictionaries,encyclopedias,glossaries) ,01 natural sciences ,Mathematics - Abstract
In this paper, the notion of an operator \gamma on a supra topological space (X,\mu ) is studied and then utilized to analyze supra \gamma -open sets. The notions of {\mu }_{\gamma }-g.closed sets on the subspace are introduced and investigated. Furthermore, some new {\mu }_{\gamma }-separation axioms are formulated and the relationships between them are shown. Moreover, some characterizations of the new functions via operator \gamma on \mu are presented and investigated. Finally, we give some properties of {S}_{(\gamma ,\beta )}-closed graph and strongly {S}_{(\gamma ,\beta )}-closed graph.
- Published
- 2020
32. On a characterization of exponential, Pearson and Pareto distributions via covariance and pseudo-covariance
- Author
-
Piotr Pawlas and Dominik Szynal
- Subjects
Exponential distribution ,Uniform distribution (continuous) ,General Mathematics ,010102 general mathematics ,Order statistic ,Pareto principle ,Characterization (mathematics) ,Covariance ,01 natural sciences ,Exponential function ,010101 applied mathematics ,Linear regression ,Applied mathematics ,0101 mathematics ,Mathematics - Abstract
Properties of linear regression of order statistics and their functions are usually utilized for the characterization of distributions. In this paper, based on such statistics, the concept of Pearson covariance and the pseudo-covariance measure of dependence is used to characterize the exponential, Pearson and Pareto distributions.
- Published
- 2020
33. Hyers-Ulam stability of a nonautonomous semilinear equation with fractional diffusion
- Author
-
José Villa-Morales
- Subjects
Mathematics::Dynamical Systems ,35b20 ,hyers-ulam stability ,General Mathematics ,45h05 ,Mathematics::Classical Analysis and ODEs ,Mathematics::Analysis of PDEs ,fractional laplacian ,01 natural sciences ,Stability (probability) ,0103 physical sciences ,Fractional diffusion ,Applied mathematics ,0101 mathematics ,Nonlinear Sciences::Pattern Formation and Solitons ,47h10 ,gronwall type inequalities ,Mathematics ,lcsh:Mathematics ,010102 general mathematics ,lcsh:QA1-939 ,35b35 ,parabolic partial differential equations ,Nonlinear Sciences::Exactly Solvable and Integrable Systems ,010307 mathematical physics ,Fractional Laplacian - Abstract
In this paper, we study the Hyers-Ulam stability of a nonautonomous semilinear reaction-diffusion equation. More precisely, we consider a nonautonomous parabolic equation with a diffusion given by the fractional Laplacian. We see that such a stability is a consequence of a Gronwall-type inequality.
- Published
- 2020
34. Existence results for nonlinear coupled system of integral equations of Urysohn Volterra-Chandrasekhar mixed type
- Author
-
Tamer Nabil
- Subjects
010101 applied mathematics ,Nonlinear system ,System of integral equations ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Mixed type ,0101 mathematics ,Fixed point ,01 natural sciences ,Chandrasekhar limit ,Mathematics - Abstract
The combined systems of integral equations have become of great importance in various fields of sciences such as electromagnetic and nuclear physics. New classes of the merged type of Urysohn Volterra-Chandrasekhar quadratic integral equations are proposed in this paper. This proposed system involves fractional Urysohn Volterra kernels and also Chandrasekhar kernels. The solvability of a coupled system of integral equations of Urysohn Volterra-Chandrasekhar mixed type is studied. To realize the existence of a solution of those mixed systems, we use the Perov’s fixed point combined with the Leray-Schauder fixed point approach in generalized Banach algebra spaces.
- Published
- 2020
35. On soft pc-separation axioms
- Author
-
Alias B. Khalaf, Nehmat K. Ahmed, and Qumri H. Hamko
- Subjects
0209 industrial biotechnology ,spaces i = 0, 1, 2 ,Astrophysics::High Energy Astrophysical Phenomena ,lcsh:Mathematics ,General Mathematics ,soft p c-open set ,54a10 ,02 engineering and technology ,54a05 ,lcsh:QA1-939 ,Separation axiom ,Algebra ,54c05 ,020901 industrial engineering & automation ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,soft p c − t i spaces i = 0, 1, 2, p c − t i ,Mathematics - Abstract
Many mathematicians defined and studied soft separation axioms and soft continuity in soft spaces by using ordinary points of a topological space X. Also, some of them studied the same concepts by using soft points. In this paper, we introduce the concepts of soft {p}_{c}-{T}_{i} and soft {p}_{c}-{T}_{i}^{\ast }, i=0,1,2 by using the concept of soft {p}_{c}-open sets in soft topological spaces. We explore several properties of such spaces. We also investigate the relationship among these spaces and provide a counter example when it is needed.
- Published
- 2020
36. Stability of an additive-quadratic-quartic functional equation
- Author
-
Gwang Hui Kim and Yang-Hi Lee
- Subjects
General Mathematics ,hyers-ulam stability ,lcsh:Mathematics ,010102 general mathematics ,fixed point theorem ,39b52 ,lcsh:QA1-939 ,01 natural sciences ,Stability (probability) ,quadratic functional equation ,010101 applied mathematics ,Quadratic equation ,Mathematics::Algebraic Geometry ,39b82 ,Quartic functional equation ,Applied mathematics ,0101 mathematics ,Mathematics ,hyperstability - Abstract
In this paper, we investigate the stability of an additive-quadratic-quartic functional equation$$\begin{align*}f(x+2y)& +f(x-2y)-2f(x+y)-2f(-x- y)-2f(x-y)-2f(y-x)\nonumber \\ &+4f(-x)+ 2f(x)-f(2y)-f(-2y)+4f(y)+4f(-y)=0 \end{align*}$$by the direct method in the sense of Găvruta.
- Published
- 2020
37. Existence results of noninstantaneous impulsive fractional integro-differential equation
- Author
-
Haribhai R. Kataria, Vishant Shah, and Prakashkumar H. Patel
- Subjects
010101 applied mathematics ,Semigroup ,Integro-differential equation ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Fixed-point theorem ,0101 mathematics ,01 natural sciences ,Mathematics - Abstract
Existence of mild solution for noninstantaneous impulsive fractional order integro-differential equations with local and nonlocal conditions in Banach space is established in this paper. Existence results with local and nonlocal conditions are obtained through operator semigroup theory using generalized Banach contraction theorem and Krasnoselskii’s fixed point theorem, respectively. Finally, illustrations are added to validate derived results.
- Published
- 2020
38. Hyers-Ulam stability of quadratic forms in 2-normed spaces
- Author
-
Jae-Hyeong Bae and Won-Gil Park
- Subjects
Pure mathematics ,Mathematics::Functional Analysis ,Mathematics::Operator Algebras ,General Mathematics ,linear 2-normed space ,hyers-ulam stability ,010102 general mathematics ,Stability (learning theory) ,Mathematics::Classical Analysis and ODEs ,39b52 ,01 natural sciences ,quadratic form ,010101 applied mathematics ,Nonlinear Sciences::Chaotic Dynamics ,Quadratic form ,39b72 ,QA1-939 ,0101 mathematics ,Nonlinear Sciences::Pattern Formation and Solitons ,Mathematics - Abstract
In this paper, we obtain Hyers-Ulam stability of the functional equations f (x + y, z + w) + f (x − y, z − w) = 2f (x, z) + 2f (y, w), f (x + y, z − w) + f (x − y, z + w) = 2f (x, z) + 2f (y, w) and f (x + y, z − w) + f (x − y, z + w) = 2f (x, z) − 2f (y, w) in 2-Banach spaces. The quadratic forms ax 2 + bxy + cy 2, ax 2 + by 2 and axy are solutions of the above functional equations, respectively.
- Published
- 2019
39. Ulam-Hyers stability of a parabolic partial differential equation
- Author
-
Sorina Anamaria Ciplea, Daniela Marian, and Nicolaie Lungu
- Subjects
Mathematics::Functional Analysis ,Mathematics::Operator Algebras ,ulam-hyers stability ,General Mathematics ,gronwall lemma ,010102 general mathematics ,Mathematical analysis ,Mathematics::Classical Analysis and ODEs ,black-scholes equation ,35l70 ,01 natural sciences ,Stability (probability) ,Parabolic partial differential equation ,010101 applied mathematics ,Nonlinear Sciences::Chaotic Dynamics ,integral inequality ,QA1-939 ,45h10 ,0101 mathematics ,Nonlinear Sciences::Pattern Formation and Solitons ,parabolic partial differential equation ,generalized ulam-hyers-rassias stability ,47h10 ,Mathematics - Abstract
The goal of this paper is to give an Ulam-Hyers stability result for a parabolic partial differential equation. Here we present two types of Ulam stability: Ulam-Hyers stability and generalized Ulam-Hyers-Rassias stability. Some examples are given, one of them being the Black-Scholes equation.
- Published
- 2019
40. Reproducing Kernel Hilbert Space and Coalescence Hidden-variable Fractal Interpolation Functions
- Author
-
Srijanani Anurag Prasad
- Subjects
coalescence ,General Mathematics ,01 natural sciences ,010305 fluids & plasmas ,symbols.namesake ,Fractal ,fractal ,0103 physical sciences ,Attractor ,QA1-939 ,0101 mathematics ,42c40 ,41a15 ,Mathematics ,Coalescence (physics) ,28a80 ,010102 general mathematics ,Mathematical analysis ,reproducing kernel ,hilbert space ,65t60 ,Hilbert space ,interpolation ,attractor ,Hidden variable theory ,symbols ,42c10 ,Reproducing kernel Hilbert space - Abstract
Reproducing Kernel Hilbert Spaces (RKHS) and their kernel are important tools which have been found to be incredibly useful in many areas like machine learning, complex analysis, probability theory, group representation theory and the theory of integral operator. In the present paper, the space of Coalescence Hidden-variable Fractal Interpolation Functions (CHFIFs) is demonstrated to be an RKHS and its associated kernel is derived. This extends the possibility of using this new kernel function, which is partly self-affine and partly non-self-affine, in diverse fields wherein the structure is not always self-affine.
- Published
- 2019
41. Convergence and stability of Fibonacci-Mann iteration for a monotone non-Lipschitzian mapping
- Author
-
Izhar Uddin and Sajan Aggarwal
- Subjects
Fibonacci number ,monotone non-lipschitzian mapping ,General Mathematics ,010102 general mathematics ,Stability (learning theory) ,Mann iteration ,nearly asymptotically nonexpansive mapping ,Fixed-point theorem ,01 natural sciences ,fixed point theorems ,010101 applied mathematics ,54h25 ,Monotone polygon ,Convergence (routing) ,QA1-939 ,Applied mathematics ,hyperbolic metric space ,0101 mathematics ,fibonacci-mann iteration ,47h10 ,Mathematics - Abstract
In this paper, we prove strong convergence and Δ−convergence of Fibonacci-Mann iteration for a monotone non-Lipschitzian mapping (i.e. nearly asymptotically nonexpansive mapping) in partially ordered hyperbolic metric space. Moreover, we prove stability of Fibonacci-Mann iteration. Further, we construct a numerical example to illustrate results. Our results simultaneously generalize the results of Alfuraidan and Khamsi [Bull. Aust. Math. Soc., 2017, 96, 307–316] and Schu [J. Math. Anal. Appl., 1991, 58, 407–413].
- Published
- 2019
42. Hyers–Ulam stability of a coupled system of fractional differential equations of Hilfer–Hadamard type
- Author
-
Akbar Zada, Jehad Alzabut, and Manzoor Ahmad
- Subjects
kransnoselskii’s fixed point theorem ,General Mathematics ,hyers-ulam stability ,010102 general mathematics ,34b27 ,implicit switched coupled systems ,34a08 ,Type (model theory) ,01 natural sciences ,Stability (probability) ,010101 applied mathematics ,hilfer-hadamard type fractional differential equations ,Hadamard transform ,QA1-939 ,Applied mathematics ,0101 mathematics ,Fractional differential ,26a33 ,Mathematics - Abstract
In this paper, existence and uniqueness of solution for a coupled impulsive Hilfer–Hadamard type fractional differential system are obtained by using Kransnoselskii’s fixed point theorem. Different types of Hyers–Ulam stability are also discussed.We provide an example demonstrating consistency to the theoretical findings.
- Published
- 2019
43. Degrees of the approximations by some special matrix means of conjugate Fourier series
- Author
-
Ewa Sylwestrzak-Maślanka, Aleksandra Rzepka, and Radosława Kranz
- Subjects
General Mathematics ,fourier series ,010102 general mathematics ,Mathematical analysis ,matrix means ,01 natural sciences ,010101 applied mathematics ,Matrix (mathematics) ,Conjugate Fourier series ,QA1-939 ,degree of approximation ,0101 mathematics ,Fourier series ,Mathematics ,42a24 - Abstract
In this paper we will present the pointwise and normwise estimations of the deviations considered by W. Łenski, B. Szal, [Acta Comment. Univ. Tartu. Math., 2009, 13, 11-24] and S. Saini, U. Singh, [Boll. Unione Mat. Ital., 2016, 9, 495-504] under general assumptions on the class considered sequences defining the method of the summability. We show that the obtained estimations are the best possible for some subclasses of Lp by constructing the suitable type of functions.
- Published
- 2019
44. Characterizations of compact operators on ℓp−type fractional sets of sequences
- Author
-
Faruk Özger
- Subjects
Pure mathematics ,General Mathematics ,010102 general mathematics ,compact operator ,02 engineering and technology ,Type (model theory) ,Compact operator ,01 natural sciences ,Fractional operator ,fractional operator ,operator norm ,gamma function ,0202 electrical engineering, electronic engineering, information engineering ,QA1-939 ,020201 artificial intelligence & image processing ,0101 mathematics ,Gamma function ,46b45 ,Operator norm ,hausdorff measure of noncompactness ,Mathematics ,47b37 - Abstract
Among the sets of sequences studied, difference sets of sequences are probably the most common type of sets. This paper considers some ℓp−type fractional difference sets via the gamma function. Although, we characterize compactness conditions on those sets using the main key of Hausdorff measure of noncompactness, we can only obtain sufficient conditions when the final space is ℓ∞. However, we use some recent results to exactly characterize the classes of compact matrix operators when the final space is the set of bounded sequences.
- Published
- 2019
45. A generalized Walsh system for arbitrary matrices
- Author
-
Steven N. Harding and Gabriel Picioroaga
- Subjects
Algebra ,cuntz algebras ,General Mathematics ,Walsh function ,QA1-939 ,walsh basis ,hadamard matrix ,Mathematics - Abstract
In this paper we study in detail a variation of the orthonormal bases (ONB) of L2[0, 1] introduced in [Dutkay D. E., Picioroaga G., Song M. S., Orthonormal bases generated by Cuntz algebras, J. Math. Anal. Appl., 2014, 409(2), 1128-1139] by means of representations of the Cuntz algebra ON on L2[0, 1]. For N = 2 one obtains the classic Walsh system which serves as a discrete analog of the Fourier system. We prove that the generalized Walsh system does not always display periodicity, or invertibility, with respect to function multiplication. After characterizing these two properties we also show that the transform implementing the generalized Walsh system is continuous with respect to filter variation. We consider such transforms in the case when the orthogonality conditions in Cuntz relations are removed. We show that these transforms which still recover information (due to remaining parts of the Cuntz relations) are suitable to use for signal compression, similar to the discrete wavelet transform.
- Published
- 2019
46. Existence and Ulam stability for nonlinear implicit differential equations with Riemann-Liouville fractional derivative
- Author
-
Juan J. Nieto, Soufyane Bouriah, Mouffak Benchohra, Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización, and Universidade de Santiago de Compostela. Instituto de Matemáticas
- Subjects
riemann-liouville fractional derivative ,Differential equation ,General Mathematics ,fixed point theorem ,Fixed-point theorem ,Riemann-Liouville fractional derivative ,Existence ,01 natural sciences ,Stability (probability) ,QA1-939 ,Applied mathematics ,Initial value problem ,Uniqueness ,0101 mathematics ,26a33 ,ulam stability ,Mathematics ,Fixed point theorem ,010102 general mathematics ,existence ,Ulam stability ,uniqueness ,Fractional calculus ,010101 applied mathematics ,Nonlinear system ,Contraction principle ,initial value problem - Abstract
In this paper, we establish the existence and uniqueness of solutions for a class of initial value problem for nonlinear implicit fractional differential equations with Riemann-Liouville fractional derivative, also, the stability of this class of problem. The arguments are based upon the Banach contraction principle and Schaefer’s fixed point theorem. An example is included to show the applicability of our results The research of J.J. Nieto has been partially supported by the AEI of Spain under Grant MTM2016-75140-P and co-financed by European Community fund FEDER SI
- Published
- 2019
47. Approximation properties of Kantorovich type q-Balázs-Szabados operators
- Author
-
Esma Yıldız Özkan
- Subjects
Pure mathematics ,General Mathematics ,010102 general mathematics ,balázs-szabados operators ,Type (model theory) ,01 natural sciences ,010101 applied mathematics ,Rate of convergence ,peetre’s k-functional ,QA1-939 ,0101 mathematics ,q-calculus ,41a25 ,41a36 ,Mathematics ,rate of convergence ,41a35 - Abstract
In this paper, we introduce a new kind of q-Balázs-Szabados-Kantorovich operators called q-BSK operators. We give a weighted statistical approximation theorem and the rate of convergence of the q-BSK operators. Also, we investigate the local approximation results. Further, we give some comparisons associated with the convergence of q-BSK operators.
- Published
- 2019
48. Orthogonal stability of the generalized quadratic functional equations in the sense of Rätz
- Author
-
Laddawan Aiemsomboon and Wutiphol Sintunavarat
- Subjects
Mathematics::Functional Analysis ,Thesaurus (information retrieval) ,General Mathematics ,010102 general mathematics ,Stability (learning theory) ,primary 39b52, 39b55, 39b72 ,Sense (electronics) ,stability ,orthogonally generalized quadratic functional equation ,01 natural sciences ,010101 applied mathematics ,Algebra ,secondary 47h10, 46h25 ,QA1-939 ,0101 mathematics ,Mathematics ,Quadratic functional ,fixed point method - Abstract
Let (X, ⊥) be an orthogonality module in the sense of Rätz over a unital Banach algebra A and Y be a real Banach module over A. In this paper, we apply the alternative fixed point theorem for proving the Hyers-Ulam stability of the orthogonally generalized k-quadratic functional equation of the form a f ( k x + y ) + a f ( k x - y ) = f ( a x + a y ) + f ( a x - a y ) + ( 2 k 2 - 2 ) f ( a x ) af(kx + y) + af(kx - y) = f(ax + ay) + f(ax - ay) + \left( {2{k^2} - 2} \right)f(ax) for some |k| > 1, for all a ɛ A 1 := {u ɛ A||u|| = 1} and for all x, y ɛ X with x⊥y, where f maps from X to Y.
- Published
- 2019
49. Slice holomorphic solutions of some directional differential equations with bounded L-index in the same direction
- Author
-
Liana Smolovyk, Andriy Bandura, and Oleh Skaskiv
- Subjects
Index (economics) ,bounded l-index ,Differential equation ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Holomorphic function ,32a37 ,bounded l-index in direction ,32a17 ,32a10 ,01 natural sciences ,slice function ,30a05 ,Bounded function ,holomorphic function ,30h99 ,0103 physical sciences ,QA1-939 ,directional differential equation ,010307 mathematical physics ,0101 mathematics ,Mathematics ,bounded index - Abstract
In the paper we investigate slice holomorphic functions F : ℂ n → ℂ having bounded L-index in a direction, i.e. these functions are entire on every slice {z 0 + t b : t ∈ℂ} for an arbitrary z 0 ∈ℂ n and for the fixed direction b ∈ℂ n \ {0}, and (∃m 0 ∈ ℤ+) (∀m ∈ ℤ+) (∀z ∈ ℂ n ) the following inequality holds | ∂ b m F ( z ) | m ! L m ( z ) ≤ max 0 ≤ k ≤ m 0 | ∂ b k F ( z ) | k ! L k ( z ) , {{\left| {\partial _{\bf{b}}^mF(z)} \right|} \over {m!{L^m}(z)}} \le \mathop {\max }\limits_{0 \le k \le {m_0}} {{\left| {\partial _{\bf{b}}^kF(z)} \right|} \over {k!{L^k}(z)}}, where L : ℂ n → ℝ+ is a positive continuous function, ∂ b F ( z ) = d d t F ( z + t b ) | t = 0 , ∂ b p F = ∂ b ( ∂ b p - 1 F ) {\partial _{\bf{b}}}F(z) = {d \over {dt}}F\left( {z + t{\bf{b}}} \right){|_{t = 0}},\partial _{\bf{b}}^pF = {\partial _{\bf{b}}}\left( {\partial _{\bf{b}}^{p - 1}F} \right) for p ≥ 2. Also, we consider index boundedness in the direction of slice holomorphic solutions of some partial differential equations with partial derivatives in the same direction. There are established sufficient conditions providing the boundedness of L-index in the same direction for every slie holomorphic solutions of these equations.
- Published
- 2019
50. Stability of an AQCQ functional equation in non-Archimedean (n,β)-normed spaces
- Author
-
Guofen Liu, Xiuzhong Yang, and Yachai Liu
- Subjects
aqcq functional equation ,Mathematics::Functional Analysis ,Pure mathematics ,Mathematics::Operator Algebras ,General Mathematics ,hyers-ulam-rassias stability ,010102 general mathematics ,01 natural sciences ,Stability (probability) ,010101 applied mathematics ,39b82 ,39b72 ,Functional equation ,QA1-939 ,0101 mathematics ,non-archimedean (n, β)-normed space ,Mathematics - Abstract
In this paper, we adopt direct method to prove the Hyers-Ulam-Rassias stability of an additivequadratic-cubic-quartic functional equationf(x+2y)+f(x−2y)=4f(x+y)+4f(x−y)−6f(x)+f(2y)+f(−2y)−4f(y)−4f(−y)$$f(x + 2y) + f(x - 2y) = 4f(x + y) + 4f(x - y) - 6f(x) + f(2y) + f( - 2y) - 4f(y) - 4f( - y)$$in non-Archimedean (n,β)-normed spaces.
- Published
- 2019
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