49 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. '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
4. 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
5. 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
6. 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
7. 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
8. 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
9. 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
10. 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
11. 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
12. 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
13. 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
14. Stability of an additive-quadratic-quartic functional equation
- Author
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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
15. Hyers-Ulam stability of quadratic forms in 2-normed spaces
- Author
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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
16. Ulam-Hyers stability of a parabolic partial differential equation
- Author
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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
17. Reproducing Kernel Hilbert Space and Coalescence Hidden-variable Fractal Interpolation Functions
- Author
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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
18. Convergence and stability of Fibonacci-Mann iteration for a monotone non-Lipschitzian mapping
- Author
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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
19. Hyers–Ulam stability of a coupled system of fractional differential equations of Hilfer–Hadamard type
- Author
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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
20. 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
21. A generalized Walsh system for arbitrary matrices
- Author
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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
22. Approximation properties of Kantorovich type q-Balázs-Szabados operators
- Author
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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
23. Approximate property of a functional equation with a general involution
- Author
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Won-Gil Park and Jae-Hyeong Bae
- Subjects
Involution (mathematics) ,Pure mathematics ,Banach space ,General Mathematics ,lcsh:Mathematics ,involution ,lcsh:QA1-939 ,approximation ,Mathematics - Abstract
In this paper, we prove the Hyers-Ulam stability of the functional equation f(x + y, z + w) + f(x + σ(y),z + τ(w)) = 2f(x, z) + 2f(y, w), where σ, τ are involutions.
- Published
- 2018
24. Certain Laplace transforms of convolution type integrals involving product of two special pFp functions
- Author
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Rakesh K. Parmar, Arjun K. Rathie, and Gradimir V. Milovanović
- Subjects
Pure mathematics ,Convolution type integrals ,Laplace transform ,33C90 ,General Mathematics ,010103 numerical & computational mathematics ,02 engineering and technology ,Kummer’s summation theorem ,Type (model theory) ,01 natural sciences ,Watson’s summation theorem ,Convolution ,Dougall’s theorem ,0202 electrical engineering, electronic engineering, information engineering ,Gauss’s summation theorem ,Gauss’s second summation theorem ,0101 mathematics ,Dixon’s summation theorem ,Primary 33C20 ,Mathematics ,lcsh:Mathematics ,lcsh:QA1-939 ,Secondary 33C05 ,Product (mathematics) ,Bailey’s summation theorem ,020201 artificial intelligence & image processing ,Whipple’s first and second summation theorems - Abstract
Recently the authors obtained several Laplace transforms of convolution type integrals involving Kummer’s function 1F1 [Appl. Anal. Discrete Math., 2018, 12(1), 257-272]. In this paper, the authors aim at presenting several new and interesting Laplace transforms of convolution type integrals involving product of two special generalized hypergeometric functions pFp by employing classical summation theorems for the series 2F1, 3F2, 4F3 and 5F4 available in the literature.
- Published
- 2018
25. Approximation solvability for a system of implicit nonlinear variational inclusions with Η-monotone operators
- Author
-
Jong Kyu Kim and Muhammad Iqbal Bhat
- Subjects
Iterative method ,General Mathematics ,iterative algorithm and convergence analysis ,lcsh:Mathematics ,010102 general mathematics ,47H06 ,resolvent operator ,lcsh:QA1-939 ,01 natural sciences ,010101 applied mathematics ,Nonlinear system ,Monotone polygon ,A- and H-monotone operators ,Resolvent operator ,Applied mathematics ,semi-inner product space ,0101 mathematics ,49J40 ,system of nonlinear implicit variational inclusion problem ,Mathematics ,49J53 - Abstract
In this paper, we introduce and study a new system of variational inclusions which is called a system of nonlinear implicit variational inclusion problems with A-monotone and H-monotone operators in semi-inner product spaces. We define the resolvent operator associated with A-monotone and H-monotone operators and prove its Lipschitz continuity. Using resolvent operator technique, we prove the existence and uniqueness of solution for this new system of variational inclusions. Moreover, we suggest an iterative algorithm for approximating the solution of this system and discuss the convergence analysis of the sequences generated by the iterative algorithm under some suitable conditions.
- Published
- 2018
26. On trigonometric approximation of functions in the Lq norm
- Author
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Ram N. Mohapatra and Bogdan Szal
- Subjects
class Lip (β ,q) ,General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,trigonometric approximation ,lcsh:QA1-939 ,01 natural sciences ,010101 applied mathematics ,Norm (mathematics) ,Applied mathematics ,0101 mathematics ,Trigonometry ,Lq norm ,42A10 ,41A25 ,Mathematics - Abstract
In this paper we obtain a degree of approximation of functions in Lq by operators associated with their Fourier series using integral modulus of continuity. These results generalize many known results and are proved under less stringent conditions on the infinite matrix.
- Published
- 2018
27. Second order evolution equations with nonlocal conditions
- Author
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Mouffak Benchohra, Noreddine Rezoug, Juan J. Nieto, and Universidade de Santiago de Compostela. Departamento de Análise Matemática, Estatística e Optimización
- Subjects
Evolution system ,Second order differential equations ,Second order diferential equations ,evolution system ,General Mathematics ,nonlocal condition ,lcsh:Mathematics ,010102 general mathematics ,Nonlocal condition ,010103 numerical & computational mathematics ,lcsh:QA1-939 ,01 natural sciences ,34G20 ,Hausdorff’s measures of noncompactness ,Order (business) ,Fréchet space ,Mild solution ,mild solution ,Applied mathematics ,0101 mathematics ,Mathematics - Abstract
In this paper, we shall establish sufficient conditions for the existence of solutions for second order semilinear functional evolutions equation with nonlocal conditions in Fréchet spaces. Our approach is based on the concepts of Hausdorff measure, noncompactness and Tikhonoff’s fixed point theorem. We give an example for illustration.
- Published
- 2017
28. Some fixed point results on G-metric and Gb-metric spaces
- Author
-
Jamshaid Ahmad, Sami Ullah Khan, Zead Mustafa, Mohammed M. M. Jaradat, and Muhammad Arshad
- Subjects
Discrete mathematics ,G-metric space ,General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,Xed point ,Fixed point ,Fixed-point property ,lcsh:QA1-939 ,01 natural sciences ,010101 applied mathematics ,Metric space ,Isolated point ,Schauder fixed point theorem ,54H25 ,fixed point ,JS-G-contraction ,Metric (mathematics) ,Interpolation space ,0101 mathematics ,Kakutani fixed-point theorem ,47H10 ,Mathematics ,Gb-metric space - Abstract
The purpose of this paper is to prove some fixed point results using JS-G-contraction on G-metric spaces, also to prove some fixed point results on Gb-complete metric space for a new contraction. Our results extend and improve some results in the literature. Moreover, some examples are presented to illustrate the validity of our results.
- Published
- 2017
29. On generalized Baskakov-Durrmeyer-Stancu type operators
- Author
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Purshottam Narain Agrawal, Zoltán Finta, and Angamuthu Sathish Kumar
- Subjects
Pure mathematics ,General Mathematics ,Microlocal analysis ,Spectral theorem ,Type (model theory) ,01 natural sciences ,Fourier integral operator ,Baskakov-Durrmeyer-Stancu operators ,Lipschitz type space ,A-statistical convergence ,0101 mathematics ,41A25 ,Mathematics ,lcsh:Mathematics ,010102 general mathematics ,Operator theory ,lcsh:QA1-939 ,010101 applied mathematics ,26A15 ,26A16 ,Baskakov operator ,Rate of convergence ,modulus of smoothness ,41A36 ,Operator norm ,rate of convergence - Abstract
In this paper, we study some local approximation properties of generalized Baskakov-Durrmeyer-Stancu operators. First, we establish a recurrence relation for the central moments of these operators, then we obtain a local direct result in terms of the second order modulus of smoothness. Further, we study the rate of convergence in Lipschitz type space and the weighted approximation properties in terms of the modulus of continuity, respectively. Finally, we investigate the statistical approximation property of the new operators with the aid of a Korovkin type statistical approximation theorem.
- Published
- 2017
30. Some Convergence Properties of the Sum of Gaussian Functionals
- Author
-
Agnieszka Wałachowska
- Subjects
Gaussian functionals ,General Mathematics ,Gaussian ,lcsh:Mathematics ,010102 general mathematics ,010103 numerical & computational mathematics ,lcsh:QA1-939 ,01 natural sciences ,Gaussian random field ,symbols.namesake ,Convergence (routing) ,symbols ,Applied mathematics ,0101 mathematics ,almost sure convergence ,Mathematics - Abstract
In the paper, some aspects of the convergence of series of dependent Gaussian sequences problem are solved. The necessary and sufficient conditions for the convergence of series of centered dependent indicators are obtained. Some strong convergence results for weighted sums of Gaussian functionals are discussed.
- Published
- 2016
31. Painlevé Equation PII and Strongly Normal Extensions
- Author
-
Sofiane El-Hadi Miri
- Subjects
strongly normal extensions ,Pure mathematics ,Painlevé equation PII ,General Mathematics ,lcsh:Mathematics ,Mathematical analysis ,differential algebra ,lcsh:QA1-939 ,Mathematics - Abstract
The aim of this paper is to show that if F is a differential field and y is a PII transcendent such that tr.deg.F 〈y〉 = 2, then every constant in F〈y〉 is in F. We also show that in this case, F〈y〉 is not contained in any strongly normal extension.
- Published
- 2016
32. Generalized Binomial Convolution of the mth Powers of the Consecutive Integers with the General Fibonacci Sequence
- Author
-
Emrah Kılıç, Ilker Akkus, Yücel Türker Ulutaş, Neşe Ömür, TOBB ETU, Faculty of Science and Literature, Depertment of Mathematics, TOBB ETÜ, Fen Edebiyat Fakültesi, Matematik Bölümü, Kılıç, Emrah, and Kırıkkale Üniversitesi
- Subjects
Discrete mathematics ,Fibonacci number ,Binomial (polynomial) ,Mathematics::Commutative Algebra ,Binomial approximation ,General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,Integer sequence ,Stirling numbers of the second kind ,lcsh:QA1-939 ,01 natural sciences ,general Fibonacci sequence ,Convolution ,010101 applied mathematics ,binomial convolution ,0101 mathematics ,Mathematics - Abstract
In this paper, we consider Gauthier’s generalized convolution and then define its binomial analogue as well as alternating binomial analogue. We formulate these convolutions and give some applications of them.
- Published
- 2016
33. More on Ostrowski Type Inequalities for some S-Convex Functions in the Second Sense
- Author
-
Zeng Liu
- Subjects
Hölder's inequality ,convex function ,Pure mathematics ,Inequality ,General Mathematics ,media_common.quotation_subject ,Hölder inequality ,lcsh:Mathematics ,010102 general mathematics ,Ostrowski type inequality ,Sense (electronics) ,Type (model theory) ,lcsh:QA1-939 ,01 natural sciences ,010101 applied mathematics ,s-convex function ,0101 mathematics ,Convex function ,media_common ,Mathematics - Abstract
Some Ostrowski type inequalities for functions whose second derivatives in absolute value at certain powers are s-convex in the second sense are established. Two mistakes in a recently published paper are pointed out and corrected.
- Published
- 2016
34. Stability of n-Dimensional Additive Functional Equation in Generalized 2-Normed Space
- Author
-
M. Arunkumar
- Subjects
Mathematics::Functional Analysis ,additive functional equation ,N dimensional ,Mathematics::Operator Algebras ,General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,Mathematical analysis ,lcsh:QA1-939 ,01 natural sciences ,Stability (probability) ,generalized Ulam-Hyers-Rassias stability ,010101 applied mathematics ,Functional equation ,0101 mathematics ,Normed vector space ,Mathematics - Abstract
In this paper, the author established the general solution and generalized Ulam-Hyers-Rassias stability of n-dimensional additive functional equationin generalized 2-normed space.
- Published
- 2016
35. Common Fixed Point Theorems for Mappings under (CLRS)-Property in Partial Metric Spaces
- Author
-
Mohammad Imdad, K. V. Siva Parvathi, and K. P. R. Rao
- Subjects
Discrete mathematics ,Pure mathematics ,Property (philosophy) ,General Mathematics ,w-compatible mappings ,lcsh:Mathematics ,010102 general mathematics ,lcsh:QA1-939 ,01 natural sciences ,(CLRS)-property ,partial metric ,010101 applied mathematics ,Metric space ,Common fixed point ,0101 mathematics ,Mathematics - Abstract
In this paper, we introduce the concept of (CLRS)-property for mappings F : X × X→X and S : X → X (wherein X stands for a partial metric space) and utilize the same to prove two common fixed point theorems for two pairs of mappings in partial metric spaces. We also furnish two examples to illustrate our main theorems.
- Published
- 2016
36. C3-Modules
- Author
-
Shahabaddin Ebrahimi Atani, Mehdi Khoramdel, and Saboura Dolati Pish Hesari
- Subjects
Mathematics::Commutative Algebra ,General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,C3-modules ,lcsh:QA1-939 ,01 natural sciences ,010101 applied mathematics ,C3-envelope ,0101 mathematics ,Mathematics::Representation Theory ,quasi-continiuous modules ,C2-modules ,C3- covers - Abstract
In this paper, we provide some characterizations of semisimple rings, right V-rings, right hereditary and regular right FGC-rings in terms of C3-modules. The notions of C3-envelope and C3-cover are introduced.
- Published
- 2016
37. Corrigendum to 'Generalizations of Opial-Type Inequalities in Several Independent Variables' Published in Demonstratio Math. 4(47) (2014), 324–335
- Author
-
Josip Pečarić, Maja Andrić, Ana Barbir, and G. Roqia
- Subjects
Variables ,Willett’s inequality ,Inequality ,General Mathematics ,media_common.quotation_subject ,lcsh:Mathematics ,010102 general mathematics ,Mathematics::History and Overview ,02 engineering and technology ,Type (model theory) ,several independent variables ,Rozanova’s inequality ,lcsh:QA1-939 ,01 natural sciences ,Algebra ,020303 mechanical engineering & transports ,0203 mechanical engineering ,Opial-type inequalities ,Calculus ,0101 mathematics ,media_common ,Mathematics - Abstract
The purpose of this corrigendum is to correct an error in the earlier paper by the authors: Generalizations of Opial-type inequalities in several independent variables, Demonstratio Math.
- Published
- 2016
38. On The K-Pseudo Symmetric and Ordinary Differentiation
- Author
-
E. Łazarow and M. Turowska
- Subjects
Pure mathematics ,General Mathematics ,σ-porous set ,lcsh:Mathematics ,ordinary derivative ,lcsh:QA1-939 ,k-pseudo symmetric derivative ,Mathematics - Abstract
In 1972, S. Valenti introduced the definition of k-pseudo symmetric derivative and has shown that the set of all points of a continuous function, at which there exists a finite k-pseudo symmetric derivative but the finite ordinary derivative does not exist, is of Lebesgue measure zero. In 1993, L. Zajícek has shown that for a continuous function f, the set of all points, at which f is symmetrically differentiable but no differentiable, is σ-(1 - ε) symmetrically porous for every ε > 0. The question arises: can we transferred the Zajícek’s result to the case of the k-pseudo symmetric derivative?In this paper, we shall show that for each 0 < ε < 1 the set of all points of a continuous function, at which there exists a finite k-pseudo symmetric derivative but the finite ordinary derivative does not exist, is σ-(1 - ε)-porous.
- Published
- 2016
39. Intuitionistic fuzzy almost Cauchy–Jensen mappings
- Author
-
M. E. Gordji and Sadegh Abbaszadeh
- Subjects
Hyers–Ulam stability ,46S40 ,Pure mathematics ,Cauchy–Jensen mapping ,General Mathematics ,lcsh:Mathematics ,47S40 ,39B52 ,Cauchy distribution ,Intuitionistic fuzzy ,010103 numerical & computational mathematics ,lcsh:QA1-939 ,01 natural sciences ,010305 fluids & plasmas ,34K36 ,0103 physical sciences ,39B82 ,0101 mathematics ,26E50 ,intuitionistic fuzzy Banach space ,Mathematics - Abstract
In this paper, we first investigate the Hyers–Ulam stability of the generalized Cauchy–Jensen functional equation of p-variable f(∑i=1paixi)=∑i=1paif(xi)$f\left(\sum\nolimits_{i = 1}^p {a_i x_i } \right) = \sum\nolimits_{i = 1}^p {a_i f(x_i )}$ in an intuitionistic fuzzy Banach space. Then, we conclude the results for Cauchy–Jensen functional equation of p-variable f(x1+⋯+xpp)=1p(f(x1)+⋯+f(xp))$f\left( {{\textstyle{{x_1 + \cdots + x_p } \over p}}} \right) = {1 \over p}(f(x_1 ) + \cdots + f(x_p ))$ . Next, we discuss the intuitionistic fuzzy continuity of Cauchy–Jensen mappings.
- Published
- 2016
40. A Suzuki type unique common fixed point theorem for two pairs of hybrid maps under a new condition in partial metric spaces
- Author
-
K. P. R. Rao, Mohammad Imdad, and K. R. K. Rao
- Subjects
Discrete mathematics ,General Mathematics ,Injective metric space ,lcsh:Mathematics ,010102 general mathematics ,partial metric space ,multi-valued maps ,lcsh:QA1-939 ,01 natural sciences ,condition (W.C.C) ,Convex metric space ,Intrinsic metric ,010101 applied mathematics ,Combinatorics ,Metric space ,Hausdorff distance ,54H25 ,Metric (mathematics) ,partial Hausdorff metric ,Metric map ,0101 mathematics ,Metric differential ,47H10 ,Mathematics - Abstract
In this paper, we introduce a new condition namely: condition (W.C.C.) and utilize the same to prove a Suzuki type unique common fixed point theorem for two hybrid pairs of mappings in partial metric spaces employing the partial Hausdorff metric which generalizes several known results of the existing literature proved in metric and partial metric spaces.
- Published
- 2016
41. Localization results for the non-truncated max-product sampling operators based on Fejér and sinc-type kernels
- Author
-
Sorin G. Gal and Lucian Coroianu
- Subjects
Discrete mathematics ,Sinc function ,General Mathematics ,local direct result ,lcsh:Mathematics ,010102 general mathematics ,Primary 41A36, 41A40 ,Secondary 41A27, 41A20, 94A12 ,Sampling (statistics) ,Type (model theory) ,lcsh:QA1-939 ,01 natural sciences ,signal theory ,010101 applied mathematics ,Fejér kernel ,Product (mathematics) ,Lipschitz function on subintervals ,Applied mathematics ,Signal theory ,Fejér-type kernel ,max-product sampling operators ,sinc (Whitaker-type) kernel ,0101 mathematics ,Mathematics ,localization result - Abstract
In this paper, we obtain strong localization results and local direct results in the approximation of continuous functions by the non-truncated max-product sampling operators based on Fejér and sinc (Wittaker)-type kernels. These operators present potential applications in signal theory.
- Published
- 2016
42. On Existence of Solutions of Impulsive Nonlinear Functional Neutral Integro-Differential Equations With Nonlocal Condition
- Author
-
M. B. Dhakne and Rupali S. Jain
- Subjects
Mathematics::Functional Analysis ,integro-differential equation ,Differential equation ,General Mathematics ,nonlocal condition ,lcsh:Mathematics ,Mathematical analysis ,Fixed point ,lcsh:QA1-939 ,Nonlinear system ,functional ,impulsive ,fixed point ,Integro-differential equation ,neutral ,Mathematics - Abstract
In the present paper, we investigate the existence, uniqueness and continuous dependence of mild solutions of an impulsive neutral integro-differential equations with nonlocal condition in Banach spaces. We use Banach contraction principle and the theory of fractional power of operators to obtain our results.
- Published
- 2015
43. Free Algebras Over a Poset in Varieties of Łukasiewicz–Moisil Algebras
- Author
-
C. Gallardo and A. Figallo Orellano
- Subjects
Pure mathematics ,Jordan algebra ,Mathematics::Combinatorics ,General Mathematics ,lcsh:Mathematics ,Subalgebra ,Non-associative algebra ,MV-algebra ,Łukasiewicz-Moisil algebras ,lcsh:QA1-939 ,Cayley–Dickson construction ,algebras ,Interior algebra ,Division algebra ,free algebras over a poset ,Generalized Kac–Moody algebra ,Mathematics - Abstract
A general construction of the free algebra over a poset in varieties finitely generated is given in [8]. In this paper, we apply this to the varieties of Łukasiewicz-Moisil algebras, giving a detailed description of the free algebra over a finite poset (X, ≤) , Freen((X, ≤)). As a consequence of this description, the cardinality of Freen((X, ≤)). is computed for special posets.
- Published
- 2015
44. A Generalized Common Fixed Point Theorem under an Implicit Relation
- Author
-
D. Surekha and T. Phaneendra
- Subjects
Discrete mathematics ,Pure mathematics ,orbitally complete metric space ,implicit-type relation ,Relation (database) ,General Mathematics ,lcsh:Mathematics ,common fixed point ,weakly compatible maps ,lcsh:QA1-939 ,property E.A ,Common fixed point ,Common fixed point theorem ,Mathematics - Abstract
An extended generalization of recent result of Kikina and Kikina (2011) has been established through the notions of weak compatibility and the property E.A., under an implicit-type relation and restricted orbital completeness of the space. The result of this paper also extends and generalizes that of Imdad and Ali (2007).
- Published
- 2015
45. Existence of Solutions for Higher Order Bvp with Parameters via Critical Point Theory
- Author
-
Bogdan Przeradzki and Mariusz Jurkiewicz
- Subjects
Critical point (thermodynamics) ,Order (business) ,General Mathematics ,critical point theory ,lcsh:Mathematics ,Mathematical analysis ,multidimensional spectrum ,Lidstone BVP ,Palais-Smale condition ,lcsh:QA1-939 ,Mathematics - Abstract
This paper is concerned with the existence of at least one solution of the nonlinear 2k-th order BVP. We use the Mountain Pass Lemma to get an existence result for the problem, whose linear part depends on several parameters.
- Published
- 2015
46. On Derivations of Operator Algebras with Involution
- Author
-
Nejc Širovnik and Joso Vukman
- Subjects
Discrete mathematics ,Pure mathematics ,Banach space ,Jordan derivation ,General Mathematics ,lcsh:Mathematics ,Semiprime ring ,Hilbert space ,derivation ,lcsh:QA1-939 ,Operator space ,semiprime ring ,ring ,Linear map ,prime ring ,standard operator algebra ,symbols.namesake ,Operator algebra ,and phrases ring ,Bounded function ,Prime ring ,symbols ,Mathematics - Abstract
The purpose of this paper is to prove the following result. Let X be a complex Hilbert space, let L(X) be an algebra of all bounded linear operators on X and let A(X) ⊂ L(X) be a standard operator algebra, which is closed under the adjoint operation. Suppose there exists a linear mapping D : A(X) → L(X) satisfying the relation 2D(AA*A) = D(AA*)A + AA*D(A) + D(A)A*A + AD(A*A) for all A ∈ A(X). In this case, D is of the form D(A) = [A,B] for all A ∈ A(X) and some fixed B ∈ L(X), which means that D is a derivation.
- Published
- 2014
47. New Geometric Interpretation of Quaternionic Fueter Functions
- Author
-
Wiesław Królikowski
- Subjects
Fueter regular function (quaternionic analysis) ,Pure mathematics ,Mathematics::Complex Variables ,General Mathematics ,lcsh:Mathematics ,Mathematical analysis ,and phrases fundamental 2-form ,Kähler manifold ,lcsh:QA1-939 ,Quaternionic analysis ,Interpretation (model theory) ,almost Kähler manifold (complex analysis) ,Mathematics::Differential Geometry ,Mathematics - Abstract
Introduction It is interesting that using the properties of quaternionic regular functions in the sense of Fueter, one can obtain the significant results in complex analysis (see, e.g. [1], [3]). There are many amazing relations between quaternionic functions and some objects of complex analysis. This paper is devoted to show one of them, namely that there is a correspondence between quaternionic regular functions in the sense of Fueter and fundamental 2-forms on a 4-dimensional almost Kahler manifold.
- Published
- 2014
48. Radical Transversal Lightlike Submanifolds of Indefinite Para-Sasakian Manifolds
- Author
-
S. S. Shukla and Akhilesh Yadav
- Subjects
Pure mathematics ,degenerate metric ,screen distribution ,Mathematics::Complex Variables ,General Mathematics ,lcsh:Mathematics ,Mathematical analysis ,Radial distribution ,lcsh:QA1-939 ,and phrases semi-Riemannian manifold ,General Relativity and Quantum Cosmology ,Transversal (combinatorics) ,lightlike transversal vector bundle ,Gauss and Weingarten formulae ,radical distribution ,Mathematics::Differential Geometry ,screen transversal vector bundle ,Nuclear Experiment ,Mathematics::Symplectic Geometry ,Mathematics - Abstract
In this paper, we study radical transversal lightlike submanifolds and screen slant radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds giving some non-trivial examples of these submanifolds. Integrability conditions of distributions D and RadTM on radical transversal lightlike submanifolds and screen slant radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds, have been obtained. We also study totally contact umbilical radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds.
- Published
- 2014
49. Generalizations of Opial-Type Inequalities in Several Independent Variables
- Author
-
Maja Andrić, Ana Barbir, Gholam Roqia, and Josip Pečarić
- Subjects
Pure mathematics ,Variables ,Willett’s inequality ,Inequality ,General Mathematics ,media_common.quotation_subject ,lcsh:Mathematics ,Opial-type inequalities ,Willett's inequality ,Rozanova's inequality ,several independent variables ,Type (model theory) ,Rozanova’s inequality ,lcsh:QA1-939 ,Calculus ,and phrases Opial-type inequalities ,media_common ,Mathematics - Abstract
In this paper, we consider Willett’s and Rozanova’s generalizations of Opial’s inequality and extend them to inequalities in several independent variables. Also, we present some new Opial-type inequalities in several independent variables.
- Published
- 2014
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