64 results
Search Results
2. Fixed point theorem for new type of auxiliary functions
- Author
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Vishal Gupta, Arslan Hojat Ansari, and Naveen Mani
- Subjects
Pure mathematics ,021103 operations research ,metric spaces ,General Mathematics ,0211 other engineering and technologies ,Fixed-point theorem ,02 engineering and technology ,Auxiliary function ,Type (model theory) ,01 natural sciences ,010101 applied mathematics ,54h25 ,fixed point ,auxiliary function ,QA1-939 ,0101 mathematics ,47h10 ,Mathematics - Abstract
In this paper, we present some fixed point results satisfying generalized contractive condition with new auxiliary function in complete metric spaces. More precisely, the structure of the paper is the following. In the first section, we present some useful notions and results. The main aim of second section is to establish some new fixed point results in complete metric spaces. Finally, in the third section, we show the validity and superiority of our main results by suitable example. Also, as an application of our main result, some interesting corollaries have been included, which make our concepts and results effective. Our main result generalizes some well known existing results in the literature.
- Published
- 2020
3. Initial coefficient bounds for certain class of meromorphic bi-univalent functions
- Author
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Ahmad Zireh and Safa Salehian
- Subjects
Class (set theory) ,Pure mathematics ,Mathematics::Complex Variables ,General Mathematics ,010102 general mathematics ,020206 networking & telecommunications ,02 engineering and technology ,30c45 ,30c50 ,01 natural sciences ,meromorphic bi-univalent functions ,0202 electrical engineering, electronic engineering, information engineering ,QA1-939 ,coefficient estimates ,meromorphic functions ,0101 mathematics ,Mathematics ,Meromorphic function - Abstract
In this paper, we introduce and investigate an interesting subclass of meromorphic bi-univalent functions defined on Δ = {z ∈ ℂ: 1 < |z| < ∞}. For functions belonging to this class, estimates on the initial coefficients are obtained. The results presented in this paper generalize and improve some recent works.
- Published
- 2019
4. Properties and Inference for a New Class of Generalized Rayleigh Distributions with an Application
- Author
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Hayrinisa Demirci Biçer and Kırıkkale Üniversitesi
- Subjects
62e20 ,021103 operations research ,Generalized Rayleigh distribution ,General Mathematics ,Maximum likelihood ,0211 other engineering and technologies ,Shannon entropy ,Inference ,02 engineering and technology ,Least-square estimate ,01 natural sciences ,New class ,Maximum likelihood estimate ,010104 statistics & probability ,symbols.namesake ,Alpha power transformation ,symbols ,QA1-939 ,Applied mathematics ,0101 mathematics ,Rayleigh scattering ,Mathematics ,62f10 - Abstract
In the present paper, we introduce a new form of generalized Rayleigh distribution called the Alpha Power generalized Rayleigh (APGR) distribution by following the idea of extension of the distribution families with the Alpha Power transformation. The introduced distribution has the more general form than both the Rayleigh and generalized Rayleigh distributions and provides a better fit than the Rayleigh and generalized Rayleigh distributions for more various forms of the data sets. In the paper, we also obtain explicit forms of some important statistical characteristics of the APGR distribution such as hazard function, survival function, mode, moments, characteristic function, Shannon and Rényi entropies, stress-strength probability, Lorenz and Bonferroni curves and order statistics. The statistical inference problem for the APGR distribution is investigated by using the maximum likelihood and least-square methods. The estimation performances of the obtained estimators are compared based on the bias and mean square error criteria by a conducted Monte-Carlo simulation on small, moderate and large sample sizes. Finally, a real data analysis is given to show how the proposed model works in practice.
- Published
- 2019
5. Some classes of sequence spaces defined by a Musielak-Orlicz function
- Author
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Sunil K. Sharma
- Subjects
orlicz function ,sequence space ,40a05 ,46a45 ,46e30 ,paranorm space ,General Mathematics ,QA1-939 ,musielak-orlicz function ,Mathematics - Abstract
In the present paper we introduce the sequence spaces c0{ℳ, Λ , p, q}, c{ℳ, Λ, p, q} and l ∞ {ℳ, Λ, p, q} defined by a Musielak-Orlicz function ℳ = (ℳk). We study some topological properties and prove some inclusion relations between these spaces.
- Published
- 2021
6. On generalized γµ-closed sets and related continuity
- Author
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Ritu Sen
- Subjects
operation ,γµ -open set ,54c08 ,βλ)-irresolute function ,General Mathematics ,(γµ ,QA1-939 ,µ-open set ,54a10 ,γµ g-closed set ,Mathematics - Abstract
In this paper our main interest is to introduce a new type of generalized open sets defined in terms of an operation on a generalized topological space. We have studied some properties of this newly defined sets. As an application, we have introduced some weak separation axioms and discussed some of their properties. Finally, we have studied some preservation theorems in terms of some irresolute functions.
- Published
- 2021
7. Labels distance in bucket recursive trees with variable capacities of buckets
- Author
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S. Naderi, R. Kazemi, and M. H. Behzadi
- Subjects
bucket recursive trees ,depth ,General Mathematics ,trivariate generating function ,60f05 ,05c05 ,partial differential equations ,QA1-939 ,distance ,Mathematics - Abstract
The bucket recursive tree is a natural multivariate structure. In this paper, we apply a trivariate generating function approach for studying of the depth and distance quantities in this tree model with variable bucket capacities and give a closed formula for the probability distribution, the expectation and the variance. We show as j → ∞, lim-iting distributions are Gaussian. The results are obtained by presenting partial differential equations for moment generating functions and solving them.
- Published
- 2021
8. Some Existence Results for Systems of Impulsive Stochastic Differential Equations
- Author
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Tayeb Blouhi, Sliman Mekki, Juan J. Nieto, and Abdelghani Ouahab
- Subjects
General Mathematics ,010102 general mathematics ,wiener process ,stochastic differential equation ,impulsive differential equations ,01 natural sciences ,34a37 ,010101 applied mathematics ,Stochastic differential equation ,fixed point ,generalized banach space ,QA1-939 ,Applied mathematics ,0101 mathematics ,60h99 ,matrix convergent to zero ,47h10 ,Mathematics - Abstract
In this paper we study a class of impulsive systems of stochastic differential equations with infinite Brownian motions. Sufficient conditions for the existence and uniqueness of solutions are established by mean of some fixed point theorems in vector Banach spaces. An example is provided to illustrate the theory.
- Published
- 2021
9. On a new one-parameter generalization of dual-complex Jacobsthal numbers
- Author
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Anetta Szynal-Liana, Dorota Bród, and Iwona Włoch
- Subjects
Jacobsthal number ,Discrete mathematics ,Dual complex ,Generalization ,General Mathematics ,11b37 ,11b39 ,dual-complex numbers ,dual-complex jacobsthal numbers ,jacobsthal numbers ,cassini identity ,QA1-939 ,binet formula ,catalan identity ,Mathematics - Abstract
In this paper we define dual-complex numbers with generalized Jacobsthal coefficients. We introduce one-parameter generalization of dual-complex Jacobsthal numbers - dual-complex r-Jacobsthal numbers. We investigate some algebraic properties of introduced numbers, among others Binet type formula, Catalan, Cassini, d’Ocagne and Honsberger type identities. Moreover, we present the generating function, summation formula and matrix generator for these numbers. The results are generalization of the properties for the dual-complex Jacobsthal numbers.
- Published
- 2021
10. Induced star-triangle factors of graphs
- Author
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Surinder Pal Singh Kainth, R. Kumar, and Shariefuddin Pirzada
- Subjects
05c70 ,05c60 ,General Mathematics ,matching ,star-triangle factor ,Astrophysics::Cosmology and Extragalactic Astrophysics ,Star (graph theory) ,Combinatorics ,factor ,QA1-939 ,Astrophysics::Solar and Stellar Astrophysics ,Astrophysics::Earth and Planetary Astrophysics ,05c62 ,Astrophysics::Galaxy Astrophysics ,Mathematics - Abstract
An induced star-triangle factor of a graph G is a spanning subgraph F of G such that each component of F is an induced subgraph on the vertex set of that component and each component of F is a star (here star means either K1,n, n ≥ 2 or K2) or a triangle (cycle of length 3) in G. In this paper, we establish that every graph without isolated vertices admits an induced star-triangle factor in which any two leaves from different stars K1,n (n ≥ 2) are non-adjacent.
- Published
- 2021
11. Frames associated with shift invariant spaces on positive half line
- Author
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Mobin Ahmad, Neyaz Ahmad, and Owais Ahmad
- Subjects
Pure mathematics ,42c15 ,41a17 ,General Mathematics ,shift-invariant space ,walsh wavelet frame ,ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION ,43a70 ,QA1-939 ,gabor frame ,Half line ,walsh-fourier transform ,Invariant (mathematics) ,42c40 ,42a38 ,Mathematics - Abstract
In this paper, we introduce the notion of Walsh shift-invariant space and present a unified approach to the study of shift-invariant systems to be frames in L2(ℝ+). We obtain a necessary condition and three sufficient conditions under which the Walsh shift-invariant systems constitute frames for L2(ℝ+). Furthermore, we discuss applications of our main results to obtain some known conclusions about the Gabor frames and wavelet frames on positive half line.
- Published
- 2021
12. Certain classes of bi-univalent functions associated with the Horadam polynomials
- Author
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Jagadeesan Yamini, Paduvalapattana Kempegowda Mamatha, Halit Orhan, Nanjundan Magesh, and Sondekola Rudra Swamy
- Subjects
bi-convex functions ,Pure mathematics ,Mathematics::Complex Variables ,General Mathematics ,11b39 ,30c45 ,33c05 ,horadam polynomials ,30c50 ,bi-univalent functions ,33c45 ,fekete-szegő inequality ,univalent functions ,QA1-939 ,bi-starlike functions ,Mathematics - Abstract
In this paper we consider two subclasses of bi-univalent functions defined by the Horadam polynomials. Further, we obtain coefficient estimates for the defined classes.
- Published
- 2021
13. Pre-derivations and description of non-strongly nilpotent filiform Leibniz algebras
- Author
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Manuel Ladra, A. Kh. Khudoyberdiyev, K. K. Abdurasulov, and Aloberdi Sattarov
- Subjects
Pure mathematics ,General Mathematics ,Dimension (graph theory) ,derivation ,010103 numerical & computational mathematics ,Disjoint sets ,17a32 ,17b30 ,01 natural sciences ,strongly nilpotent algebra ,17a36 ,17A32, 17A36, 17B30 ,Set (abstract data type) ,Mathematics::K-Theory and Homology ,FOS: Mathematics ,QA1-939 ,[MATH]Mathematics [math] ,0101 mathematics ,Mathematics::Representation Theory ,nilpotency ,Mathematics ,pre-derivation ,characteristically nilpotent algebra ,leibniz algebra ,010102 general mathematics ,Mathematics::History and Overview ,Mathematics::Rings and Algebras ,Mathematics - Rings and Algebras ,Nilpotent ,Rings and Algebras (math.RA) ,lie algebra - Abstract
In this paper we give the description of some non-strongly nilpotent Leibniz algebras. We pay our attention to the subclass of nilpotent Leibniz algebras, which is called filiform. Note that the set of filiform Leibniz algebras of fixed dimension can be decomposed into three disjoint families. We describe the pre-derivations of filiform Leibniz algebras for the first and second families and determine those algebras in the first two classes of filiform Leibniz algebras that are non-strongly nilpotent.
- Published
- 2021
14. On λD − R0 and λD − R1 spaces
- Author
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Ennis Rosas and Sarhad F. Namiq
- Subjects
Pure mathematics ,λd−open set ,General Mathematics ,λ D−open set ,λd − r0 and λd − r1 ,54a05 ,54b05 ,λ D − R0 ,54c05 ,D − R1 ,TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY ,QA1-939 ,Mathematics - Abstract
In this paper we introduce the new types of separation axioms called λD − R0 and λD − R1 spaces, by using λD-open set. The notion λD − R0 and λD − R1 spaces are introduced and some of their properties are investigated.
- Published
- 2020
15. On some properties of split Horadam quaternions
- Author
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Dorota Bród
- Subjects
Algebra ,horadam numbers ,split horadam quaternion ,quaternion ,split quaternion ,General Mathematics ,11b37 ,QA1-939 ,Quaternion ,11r52 ,Mathematics - Abstract
In this paper we introduce and study the split Horadam quaternions. We give some identities, among others Binet’s formula, Catalan’s, Cassini’s and d’Ocagne’s identities for these numbers.
- Published
- 2020
16. Assessing the effect size of users’ consciousness for computer networks vulnerability
- Author
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Antal Joós, Bálint Nagy, and László Bognár
- Subjects
60a99 ,General Mathematics ,media_common.quotation_subject ,cyber security ,vulnerability ,Vulnerability ,simulation study ,94c99 ,QA1-939 ,users’ awareness ,computer networks ,Consciousness ,Mathematics ,media_common ,Cognitive psychology - Abstract
In this paper the conditions and the findings of a simulation study is presented for assessing the effect size of users’ consciousness to the computer network vulnerability in risky cyber attack situations at a certain business. First a simple model is set up to classify the groups of users according to their skills and awareness then probabilities are assigned to each class describing the likelihood of committing dangerous reactions in case of a cyber attack. To quantify the level of network vulnerability a metric developed in a former work is used. This metric shows the approximate probability of an infection at a given business with well specified parameters according to its location, the type of the attack, the protections used at the business etc. The findings mirror back the expected tendencies namely if the number of conscious user is on the
- Published
- 2020
17. A new parameterized logarithmic kernel function for linear optimization with a double barrier term yielding the best known iteration bound
- Author
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Saoudi Khaled and Benhadid Ayache
- Subjects
90c05 ,0209 industrial biotechnology ,021103 operations research ,Logarithm ,Linear programming ,interior point methods ,General Mathematics ,0211 other engineering and technologies ,Parameterized complexity ,90c31 ,02 engineering and technology ,Double barrier ,Term (time) ,020901 industrial engineering & automation ,kernel function ,90c51 ,QA1-939 ,Applied mathematics ,complexity bound ,[MATH]Mathematics [math] ,linear optimization ,Mathematics - Abstract
In this paper, we propose a large-update primal-dual interior point algorithm for linear optimization. The method is based on a new class of kernel functions which differs from the existing kernel functions in which it has a double barrier term. The investigation according to it yields the best known iteration bound O n log ( n ) log ( n ∈ ) \sqrt n \log (n)\log \left( {{n \over \in }} \right) for large-update algorithm with the special choice of its parameter m and thus improves the iteration bound obtained in Bai et al. [2] for large-update algorithm.
- Published
- 2020
18. Construction of Barnette graphs whose large subgraphs are non-Hamiltonian
- Author
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Mushtaq A. Shah and Shariefuddin Pirzada
- Subjects
General Mathematics ,cubic graph ,barnette graph ,planar graph ,010103 numerical & computational mathematics ,01 natural sciences ,13a99 ,010101 applied mathematics ,Combinatorics ,QA1-939 ,hamiltonian graph ,05c78 ,05c12 ,0101 mathematics ,Mathematics::Symplectic Geometry ,Hamiltonian (control theory) ,Mathematics - Abstract
Barnette’s conjecture states that every three connected cubic bipartite planar graph (CPB3C) is Hamiltonian. In this paper we show the existence of a family of CPB3C Hamiltonian graphs in which large and large subgraphs are non-Hamiltonian.
- Published
- 2019
19. On bounds of the sine and cosine along straight lines on the complex plane
- Author
-
Feng Qi
- Subjects
sloped straight line ,analysis ,General Mathematics ,complex plane ,010103 numerical & computational mathematics ,Computer Science::Computational Geometry ,01 natural sciences ,30a10 ,sine ,bound ,Computer Science::Multimedia ,QA1-939 ,Trigonometric functions ,Sine ,0101 mathematics ,cosine ,Mathematics ,Physics ,Thesaurus (information retrieval) ,Mathematical analysis ,Vertical straight line ,33b10 ,horizontal straight line ,010101 applied mathematics ,Algebra ,vertical straight line ,Complex plane ,MathematicsofComputing_DISCRETEMATHEMATICS - Abstract
In the paper, the author discusses and computes bounds of the sine and cosine along straight lines on the complex plane.
- Published
- 2019
20. Study of Γ-hyperrings by fuzzy hyperideals with respect to a t-norm
- Author
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Krisanthi Naka, Serkan Onar, Bayram Ali Ersoy, and Kostaq Hila
- Subjects
0209 industrial biotechnology ,Pure mathematics ,t-fuzzy (resp. left, right) hyperideal ,16d25 ,20n20 ,General Mathematics ,08a72 ,T-norm ,t-norm ,02 engineering and technology ,Fuzzy logic ,γ-hyperrings ,16y99 ,020901 industrial engineering & automation ,t-fuzzy quasi(bi)-hyperideal ,0202 electrical engineering, electronic engineering, information engineering ,QA1-939 ,020201 artificial intelligence & image processing ,Mathematics - Abstract
In this paper, we study the Γ-hyperrings via T-fuzzy hyperideals. By means of the use of a triangular norm T, we define, characterize and study the T-fuzzy left and right hyperideals, T-fuzzy quasi-hyperideal and bi-hyperideal in Γ-hyperrings and some related properties are investigated. Regular Γ-hyperrings are characterized in terms of T-fuzzy quasi-hyperideal and T-fuzzy bi-hyperideal. We also introduce the T-(λ, µ)-fuzzy bi-hyperideals in Γ-hyperrings and investigate some of their properties.
- Published
- 2019
21. A Tauberian theorem for the statistical generalized Nörlund-Euler summability method
- Author
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Naim L. Braha
- Subjects
symbols.namesake ,Pure mathematics ,40g15 ,General Mathematics ,Euler's formula ,symbols ,QA1-939 ,one-sided and two-sided tauberian conditions ,statistical convergence ,41a36 ,generalized nörlund-euler summability ,Mathematics - Abstract
Let (pn) and (qn) be any two non-negative real sequences with R n : = ∑ k = 0 n p k q n - k ≠ 0 ( n ∈ ) {{\rm{R}}_{\rm{n}}}: = \sum\limits_{{\rm{k}} = 0}^{\rm{n}} {{{\rm{p}}_{\rm{k}}}{{\rm{q}}_{{\rm{n}} - {\rm{k}}}}} \ne 0\,\,\,\,\left( {{\rm{n}} \in {\rm\mathbb{N}}} \right) With E n 1 {\rm{E}}_{\rm{n}}^1 − we will denote the Euler summability method. Let (xn) be a sequence of real or complex numbers and set N p , q n E n 1 : = 1 R n ∑ k = 0 n p k q n - k 1 2 k ∑ v = 0 k ( v k ) x v {\rm{N}}_{{\rm{p}},{\rm{q}}}^{\rm{n}}{\rm{E}}_{\rm{n}}^1: = {1 \over {{{\rm{R}}_{\rm{n}}}}}\sum\limits_{{\rm{k}} = 0}^{\rm{n}} {{{\rm{p}}_{\rm{k}}}{{\rm{q}}_{{\rm{n - k}}}}{1 \over {{2^{\rm{k}}}}}\sum\limits_{{\rm{v}} = 0}^{\rm{k}} {\left( {_{\rm{v}}^{\rm{k}}} \right){{\rm{x}}_{\rm{v}}}} } for n ∈ ℕ. In this paper, we present necessary and sufficient conditions under which the existence of the st− limit of (xn) follows from that of st - N p , q n E n 1 {\rm{st - N}}_{{\rm{p}},q}^{\rm{n}}{\rm{E}}_{\rm{n}}^1 − limit of (xn). These conditions are one-sided or two-sided if (xn) is a sequence of real or complex numbers, respectively.
- Published
- 2019
22. gr-n-ideals in graded commutative rings
- Author
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Farah Al-Turman, Ece Yetkin Celikel, and Khaldoun Al-Zoubi
- Subjects
Pure mathematics ,13a02 ,General Mathematics ,010102 general mathematics ,020206 networking & telecommunications ,02 engineering and technology ,Commutative ring ,gr-prime ideals ,01 natural sciences ,graded rings ,0202 electrical engineering, electronic engineering, information engineering ,QA1-939 ,0101 mathematics ,gr-n-ideals ,16w50 ,Mathematics - Abstract
Let G be a group with identity e and let R be a G-graded ring. In this paper, we introduce and study the concept of gr-n-ideals of R. We obtain many results concerning gr-n-ideals. Some characterizations of gr-n-ideals and their homogeneous components are given.
- Published
- 2019
23. The sparing number of certain graph powers
- Author
-
K. A. Germina, K. P. Chithra, and Sudev Naduvath
- Subjects
Singleton ,General Mathematics ,weak integer additive set-indexers ,sparing number of a graph ,Injective function ,Combinatorics ,integer additive set-indexers ,graph powers ,FOS: Mathematics ,QA1-939 ,Graph (abstract data type) ,Mathematics - Combinatorics ,Combinatorics (math.CO) ,05c78 ,mono-indexed elements of a graph ,Mathematics - Abstract
An integer additive set-indexer is defined as an injective function $f:V(G)\rightarrow 2^{\mathbb{N}_0}$ such that the induced function $g_f:E(G) \rightarrow 2^{\mathbb{N}_0}$ defined by $g_f (uv) = f(u)+ f(v)$ is also injective. An IASI $f$ is said to be a weak IASI if $|g_f(uv)|=max(|f(u)|,|f(v)|)$ for all $u,v\in V(G)$. A graph which admits a weak IASI may be called a weak IASI graph. The set-indexing number of an element of a graph $G$, a vertex or an edge, is the cardinality of its set-labels. The sparing number of a graph $G$ is the minimum number of edges with singleton set-labels, required for a graph $G$ to admit a weak IASI. In this paper, we study the admissibility of weak IASI by certain graph powers and their sparing numbers., 14 pages, 6 figures, submitted
- Published
- 2019
24. Fractional natural decomposition method for solving a certain class of nonlinear time-fractional wave-like equations with variable coefficients
- Author
-
Ali Khalouta and Abdelouahab Kadem
- Subjects
35a22 ,Class (set theory) ,General Mathematics ,caputo fractional derivative ,010102 general mathematics ,nonlinear time-fractional wave-like equations ,01 natural sciences ,010101 applied mathematics ,Nonlinear system ,35r11 ,34k28 ,fractional natural decomposition method ,QA1-939 ,Applied mathematics ,Decomposition method (queueing theory) ,adomian polynomials ,0101 mathematics ,26a33 ,Mathematics ,Variable (mathematics) - Abstract
In this paper, we propose a new approximate method, namely fractional natural decomposition method (FNDM) in order to solve a certain class of nonlinear time-fractional wave-like equations with variable coefficients. The fractional natural decomposition method is a combined form of the natural transform method and the Adomian decomposition method. The nonlinear term can easily be handled with the help of Adomian polynomials which is considered to be a clear advantage of this technique over the decomposition method. Some examples are given to illustrate the applicability and the easiness of this approach.
- Published
- 2019
25. Computing metric dimension of compressed zero divisor graphs associated to rings
- Author
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M. Imran Bhat and Shariefuddin Pirzada
- Subjects
Discrete mathematics ,zero-divisor graph ,General Mathematics ,010102 general mathematics ,equivalence classes ,0102 computer and information sciences ,compressed zero-divisor graph ,01 natural sciences ,metric dimension ,Metric dimension ,13a99 ,010201 computation theory & mathematics ,QA1-939 ,05c78 ,05c12 ,0101 mathematics ,Zero divisor ,Mathematics - Abstract
For a commutative ring R with 1 ≠ 0, a compressed zero-divisor graph of a ring R is the undirected graph ΓE(R) with vertex set Z(RE) \ {[0]} = RE \ {[0], [1]} defined by RE = {[x] : x ∈ R}, where [x] = {y ∈ R : ann(x) = ann(y)} and the two distinct vertices [x] and [y] of Z(RE) are adjacent if and only if [x][y] = [xy] = [0], that is, if and only if xy = 0. In this paper, we study the metric dimension of the compressed zero divisor graph ΓE(R), the relationship of metric dimension between ΓE(R) and Γ(R), classify the rings with same or different metric dimension and obtain the bounds for the metric dimension of ΓE(R). We provide a formula for the number of vertices of the family of graphs given by ΓE(R×𝔽). Further, we discuss the relationship between metric dimension, girth and diameter of ΓE(R).
- Published
- 2018
26. New classes of local almost contractions
- Author
-
Mónika Zákáany
- Subjects
Pure mathematics ,General Mathematics ,010103 numerical & computational mathematics ,01 natural sciences ,010101 applied mathematics ,coefficient of contraction ,54h25 ,QA1-939 ,0101 mathematics ,almost local contraction ,47h10 ,Mathematics ,fixed- point theorem - Abstract
Contractions represents the foundation stone of nonlinear analysis. That is the reason why we propose to unify two different type of contractions: almost contractions, introduced by V. Berinde in [2] and local contractions (Martins da Rocha and Filipe Vailakis in [7]). These two types of contractions operate in different space settings: in metric spaces (almost contractions) and semimetric spaces (for local contractions). That new type of contraction was built up in a new space setting, which is the pseudometric space. The main results of this paper represent the extension for various type of operators on pseudometric spaces, such as: generalized ALC, Ćirić-typeALC, quasi ALC, Ćirić-Reich-Rustype ALC. We propose to study the existence and uniqueness of their fixed points, and also the continuity in their fixed points, with a large number of examples for ALC-s.
- Published
- 2018
27. On extensions of Baer and quasi-Baer modules
- Author
-
Ebrahim Hashemi, Abdollah Alhevaz, and Marzieh Yazdanfar
- Subjects
Pure mathematics ,General Mathematics ,010102 general mathematics ,0102 computer and information sciences ,01 natural sciences ,16s36 ,010201 computation theory & mathematics ,16d80 ,reduced module ,quasi-baer module ,QA1-939 ,baer module ,skew monoid ring ,0101 mathematics ,16s34 ,Mathematics ,s-compatible module - Abstract
Let R be a ring, MR a module, S a monoid, ω : S → End(R) a monoid homomorphism and R * S a skew monoid ring. Then M[S] = {m1g1 + · · · + mngn | n ≥ 1, mi ∈ M and gi ∈ S for each 1 ≤ i ≤ n} is a module over R ∗ S. A module MR is Baer (resp. quasi-Baer) if the annihilator of every subset (resp. submodule) of M is generated by an idempotent of R. In this paper we impose S-compatibility assumption on the module MR and prove: (1) MR is quasi-Baer if and only if M[s]R∗S is quasi-Baer, (2) MR is Baer (resp. p.p) if and only if M[S]R∗S is Baer (resp. p.p), where MR is S-skew Armendariz, (3) MR satisfies the ascending chain condition on annihilator of submodules if and only if so does M[S]R∗S, where MR is S-skew quasi-Armendariz.
- Published
- 2018
28. Integrals of polylogarithmic functions with negative argument
- Author
-
Anthony Sofo
- Subjects
polylogarithm function ,General Mathematics ,010102 general mathematics ,TheoryofComputation_GENERAL ,33b15 ,010103 numerical & computational mathematics ,01 natural sciences ,11m06 ,Argument ,TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY ,zeta functions ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,dirichlet functions ,QA1-939 ,Computer Science::Symbolic Computation ,euler sums ,0101 mathematics ,11m32 ,Computer Science::Data Structures and Algorithms ,Mathematical economics ,Mathematics ,MathematicsofComputing_DISCRETEMATHEMATICS - Abstract
The connection between polylogarithmic functions and Euler sums is well known. In this paper we explore the representation and many connections between integrals of products of polylogarithmic functions and Euler sums. We shall consider mainly, polylogarithmic functions with negative arguments, thereby producing new results and extending the work of Freitas. Many examples of integrals of products of polylogarithmic functions in terms of Riemann zeta values and Dirichlet values will be given.
- Published
- 2018
29. A sequence adapted from the movement of the center of mass of two planets in solar system
- Author
-
Jana Fialová
- Subjects
Solar System ,Movement (music) ,General Mathematics ,sequence of points ,70f05 ,Astronomy ,solar system ,trajectory of two planets ,g-discrepancy ,Planet ,center of mass ,QA1-939 ,11k31 ,Center of mass ,Astrophysics::Earth and Planetary Astrophysics ,[MATH]Mathematics [math] ,distribution function ,Mathematics ,Sequence (medicine) - Abstract
In this paper we derive a sequence from a movement of center of mass of arbitrary two planets in some solar system, where the planets circle on concentric circles in a same plane. A trajectory of center of mass of the planets is discussed. A sequence of points on the trajectory is chosen. Distances of the points to the origin are calculated and a distribution function of a sequence of the distances is found.
- Published
- 2018
30. Performance and economic analysis of Markovian Bernoulli feedback queueing system with vacations, waiting server and impatient customers
- Author
-
Abdeldjebbar Kandouci, Abdelhak Guendouzi, and Amina Angelika Bouchentouf
- Subjects
0209 industrial biotechnology ,Mathematical optimization ,68m20 ,General Mathematics ,0211 other engineering and technologies ,Markov process ,waiting server ,cost model ,02 engineering and technology ,probability generating function ,symbols.namesake ,Bernoulli's principle ,020901 industrial engineering & automation ,QA1-939 ,Economic analysis ,bernoulli feedback ,Mathematics ,021103 operations research ,Queueing system ,90b22 ,markovian queueing models ,60k25 ,symbols ,impatience ,vacations - Abstract
This paper concerns the analysis of a Markovian queueing system with Bernoulli feedback, single vacation, waiting server and impatient customers. We suppose that whenever the system is empty the sever waits for a random amount of time before he leaves for a vacation. Moreover, the customer’s impatience timer depends on the states of the server. If the customer’s service has not been completed before the impatience timer expires, the customer leaves the system, and via certain mechanism, impatient customer may be retained in the system. We obtain explicit expressions for the steady-state probabilities of the queueing model, using the probability generating function (PGF). Further, we obtain some important performance measures of the system and formulate a cost model. Finally, an extensive numerical study is illustrated.
- Published
- 2018
31. Generalized operator for Alexander integral operator
- Author
-
H. Özlem Güney, Shigeyoshi Owa, Dicle Üniversitesi, Fen Fakültesi, Matematik Bölümü, and Güney, Hatun Özlem
- Subjects
fractional integral ,General Mathematics ,Operator (physics) ,Fractional inte-gral ,30c45 ,30c50 ,Alexander integral operator ,analytic function ,alexander integral operator ,Algebra ,Miller and Mocanu lemma ,gamma function ,Analytic function ,Gamma function ,QA1-939 ,miller and mocanu lemma ,Mathematics - Abstract
Let T n be the class of functions f which are defined by a power series f ( z ) = z + a n + 1 z n + 1 + a n 2 z n + 2 + … f\left( z \right) = z + {a_{n + 1}}{z^{n + 1}} + {a_n}2{z^{n + 2}} + \ldots for every z in the closed unit disc 𝕌 ¯ \bar {\mathbb{U}} . With m different boundary points z s, (s = 1,2,...,m), we consider α m ∈ e iβ𝒜−j−λf(𝕌), here 𝒜−j−λ is the generalized Alexander integral operator and 𝕌 is the open unit disc. Applying 𝒜−j−λ, a subclass B n (α m ,β,ρ; j, λ) of T n is defined with fractional integral for functions f. The object of present paper is to consider some interesting properties of f to be in B n (α m ,β,ρ; j, λ).
- Published
- 2020
32. Some properties of analytic functions related with Booth lemniscate
- Author
-
Ali Ebadian, Sh. Najafzadeh, and Parvaneh Najmadi
- Subjects
logarithmic coefficients ,Mathematics - Complex Variables ,General Mathematics ,010102 general mathematics ,convex ,strongly starlike ,subordination ,30c45 ,Object (computer science) ,01 natural sciences ,010101 applied mathematics ,Combinatorics ,Alpha (programming language) ,FOS: Mathematics ,QA1-939 ,starlike ,Lemniscate ,Complex Variables (math.CV) ,0101 mathematics ,univalent ,Mathematics ,Analytic function - Abstract
The object of the present paper is to study of two certain subclass of analytic functions related with Booth lemniscate which we denote by $\mathcal{BS}(\alpha)$ and $\mathcal{BK}(\alpha)$. Some properties of these subclasses are considered., Comment: 9 pages
- Published
- 2018
33. Certain classes of analytic functions defined by fractional q-calculus operator
- Author
-
N. Ravikumar
- Subjects
General Mathematics ,010102 general mathematics ,30c45 ,medicine.disease ,30c50 ,01 natural sciences ,fractional q-calculus operator ,010101 applied mathematics ,Operator (computer programming) ,univalent functions ,Calculus ,medicine ,QA1-939 ,0101 mathematics ,Calculus (medicine) ,Mathematics ,Analytic function - Abstract
In this paper, the concept of fractional q-calculus and generalized Al-Oboudi differential operator defining certain classes of analytic functions in the open disc are used. The results investigated for these classes of functions include the coefficient estimates, inclusion relations, extreme points and some more properties.
- Published
- 2018
34. On the sum of the Lah numbers and zeros of the Kummer confluent hypergeometric function
- Author
-
Feng Qi and Bai-Ni Guo
- Subjects
lah number ,Pure mathematics ,Confluent hypergeometric function ,General Mathematics ,010102 general mathematics ,sum ,secondary 05a10, 05a19, 11b65, 11b99, 30c15, 33c15, 65b10 ,kummer confluent hypergeometric function ,01 natural sciences ,Lah number ,010101 applied mathematics ,QA1-939 ,zero ,0101 mathematics ,primary 11b83 ,Mathematics - Abstract
In the paper, the authors find the sum of the Lah numbers and make sure that the Kummer confluent hypergeometric function 1F1(n+ 1; 2; z) has only n− 1real and negative zeros.
- Published
- 2018
35. On the ℒ-duality of a Finsler space with exponential metric αeβ/α
- Author
-
Gauree Shanker and Ramdayal Singh Kushwaha
- Subjects
Pure mathematics ,General Mathematics ,53b40 ,53c60 ,Duality (optimization) ,010103 numerical & computational mathematics ,Space (mathematics) ,01 natural sciences ,Exponential function ,010101 applied mathematics ,Metric (mathematics) ,QA1-939 ,0101 mathematics ,cartan space ,finsler space ,Mathematics ,exponential metric ,duality between finsler and cartan spaces - Abstract
The (α, β)-metrics are the most studied Finsler metrics in Finsler geometry with Randers, Kropina and Matsumoto metrics being the most explored metrics in modern Finsler geometry. The ℒ-dual of Randers, Kropina and Matsumoto space have been introduced in [3, 4, 5], also in recent the ℒ-dual of a Finsler space with special (α, β)-metric and generalized Matsumoto spaces have been introduced in [16, 17]. In this paper, we find the ℒ-dual of a Finsler space with an exponential metric αeβ/α, where α is Riemannian metric and β is a non-zero one form.
- Published
- 2018
36. On generalized Laguerre matrix polynomials
- Author
-
A. A. Bathanya and Raed S. Batahan
- Subjects
Pure mathematics ,Recurrence relation ,15a15 ,42c05 ,General Mathematics ,010102 general mathematics ,010103 numerical & computational mathematics ,Expression (computer science) ,01 natural sciences ,Hypergeometric distribution ,33c45 ,Matrix (mathematics) ,Matrix function ,Laguerre polynomials ,QA1-939 ,three terms recurrence relation ,laguerre matrix polynomials ,0101 mathematics ,Representation (mathematics) ,generalized hypergeometric matrix function and gamma matrix function ,Mathematics - Abstract
The main object of the present paper is to introduce and study the generalized Laguerre matrix polynomials for a matrix that satisfies an appropriate spectral property. We prove that these matrix polynomials are characterized by the generalized hypergeometric matrix function. An explicit representation, integral expression and some recurrence relations in particular the three terms recurrence relation are obtained here. Moreover, these matrix polynomials appear as solution of a differential equation.
- Published
- 2018
37. Totally geodesic property of the unit tangent sphere bundle with g-natural metrics
- Author
-
Farshad Firuzi and Esmaeil Peyghan
- Subjects
Pure mathematics ,Property (philosophy) ,General Mathematics ,010102 general mathematics ,sphere bundle ,58a10 ,totally geodesic submanifold ,53c40 ,53a45 ,01 natural sciences ,53d15 ,Tangent sphere ,Bundle ,0103 physical sciences ,QA1-939 ,Totally geodesic ,010307 mathematical physics ,Mathematics::Differential Geometry ,natural metrics ,0101 mathematics ,Unit (ring theory) ,Mathematics::Symplectic Geometry ,Mathematics - Abstract
In this paper, we consider the tangent bundle of a Riemannian manifold (M, g) with g-natural metrics and among all of these metrics, we specify those with respect to which the unit tangent sphere bundle with induced g-natural metric is totally geodesic. Also, we equip the unit tangent sphere bundle T1M with g-natural contact (paracontact) metric structures, and we show that such structures are totally geodesic K-contact (K-paracontact) submanifolds of TM, if and only if the base manifold (M, g) has positive (negative) constant sectional curvature. Moreover, we establish a condition for g-natural almost contact B-metric structures on T1Msuch that these structures be totally geodesic submanifolds of TM.
- Published
- 2018
38. Uniqueness of polynomial and differential monomial
- Author
-
V. Husna and Harina P. Waghamore
- Subjects
Polynomial ,Pure mathematics ,Monomial ,differential monomial ,polynomial ,General Mathematics ,010102 general mathematics ,01 natural sciences ,sharing values ,010101 applied mathematics ,30d35 ,QA1-939 ,meromorphic function ,Uniqueness ,0101 mathematics ,Differential (mathematics) ,Mathematics - Abstract
In this paper, we discuss the problem of meromorphic functions sharing small function and present one theorem which extend a result of K. S. Charak and Banarasi Lal [16].
- Published
- 2017
39. A result regarding monotonicity of the Gamma function
- Author
-
Pál A. Kupán, Róbert Szász, and Gyöngyvér Márton
- Subjects
Pure mathematics ,General Mathematics ,010102 general mathematics ,33b15 ,Monotonic function ,01 natural sciences ,010101 applied mathematics ,gamma function ,monotonic function ,QA1-939 ,0101 mathematics ,Gamma function ,Mathematics - Abstract
In this paper we analyze the monotony of the function ln Γ ( x ) ln ( x 2 + τ ) - ln ( x + τ ) ${{{\rm{ln}}\,\Gamma ({\rm{x}})} \over {{\rm{ln}}\,({\rm{x}}^2 + \tau) - {\rm{ln}}\,({\rm{x}} + \tau)}}$ , for τ > 0. Such functions have been used from different authors to obtain inequalities concerning the gamma function.
- Published
- 2017
40. Convolution of second order linear recursive sequences II
- Author
-
Tamás Szakács
- Subjects
linear recurrence sequences ,General Mathematics ,11b37 ,11b39 ,Convolution ,fibonacci sequence ,generating function ,QA1-939 ,Order (group theory) ,Applied mathematics ,convolution ,[MATH]Mathematics [math] ,Geometry and topology ,Mathematics - Abstract
We continue the investigation of convolutions of second order linear recursive sequences (see the first part in [1]). In this paper, we focus on the case when the characteristic polynomials of the sequences have common root.
- Published
- 2017
41. Some fixed point results for rational type and subrational type contractive mappings
- Author
-
Diana Dolićanin-Đekić, Huaping Huang, Arslan Hojat Ansari, and Stojan Radenović
- Subjects
Pure mathematics ,α-admissible mapping ,General Mathematics ,010102 general mathematics ,Type (model theory) ,Fixed point ,Topology ,01 natural sciences ,010101 applied mathematics ,μ-subadmissible mapping ,54h25 ,fixed point ,μ-subregular ,QA1-939 ,0101 mathematics ,generalized metric space ,47h10 ,Mathematics ,α-regular - Abstract
In this paper, we introduce the concepts of rational type and subrational type contractive mappings. We expand and improve some fixed point theorems obtained by Alsulami et al. (Fixed Point Theory Appl., 2015, 2015: 97). Moreover, we give an example to support our results.
- Published
- 2017
42. Properties of nearly ω-continuous multifunctions
- Author
-
S. Saranyasri, Carlos Carpintero, N. Rajesh, Jackeline Pacheco, and Ennis Rosas
- Subjects
Pure mathematics ,General Mathematics ,54c10 ,010103 numerical & computational mathematics ,01 natural sciences ,010101 applied mathematics ,54c08 ,n-closed complement ,54c05 ,QA1-939 ,0101 mathematics ,nearly ω-continuous multifunctions ,Mathematics - Abstract
Erdal Ekici has introduced and studied nearly continuous multifunctions in [5]. The purpose of the present paper is to introduce and study upper and lower nearly ω-continuous multifunctions as a weaker form of upper and lower nearly continuous multifunctions. Basic characterizations, several properties of upper and lower nearly ω-continuous multifunctions are investigated.
- Published
- 2017
43. New characterization of symmetric groups of prime degree
- Author
-
Alireza Khalili Asboei and Reza Mohammadyari
- Subjects
Pure mathematics ,20d08 ,General Mathematics ,010102 general mathematics ,Prime degree ,0211 other engineering and technologies ,021107 urban & regional planning ,02 engineering and technology ,Characterization (mathematics) ,01 natural sciences ,symmetric group ,conjugacy class length ,20d60 ,Symmetric group ,finite group ,QA1-939 ,0101 mathematics ,Mathematics - Abstract
In this paper, will show that a symmetric group of prime degree p ≥ 5 is recognizable by its order and a special conjugacy class size of (p − 1)!.
- Published
- 2017
44. Unbounded solutions of an iterative-difference equation
- Author
-
Pingping Zhang and Lin Li
- Subjects
Semi-infinite ,Differential equation ,General Mathematics ,010102 general mathematics ,existence ,37e05 ,39b12 ,01 natural sciences ,unbounded solution ,convex solution ,010101 applied mathematics ,QA1-939 ,Applied mathematics ,iterative-difference equation ,concave solution ,0101 mathematics ,Mathematics - Abstract
Unbounded solutions for the iterative-difference equation f 2 ( x ) = λ f ( x + a ) + μ x , x ∈ ℝ , \font\msbm=MSBM10$${\rm{f}}^2 ({\rm{x}}) = \lambda {\rm{f}}({\rm{x}} + {\rm{a}}) + \mu {\rm{x}},\;\;\;{\rm{x}} \in {\msbm R},$$ have been considered in [Continuous solutions of an iterative-difference equation and Brillouët problem, Publ. Math. Debrecen, 78 (2011), 613–624], where λ, μ, a are real constants. In this paper, we continue to study the solutions not being included there, and further give the convex and concave ones. Finally, continuous solutions of this equation with an extra item were also given, which continuously depend on the parameter a.
- Published
- 2017
45. Common fixed point theorems for contractive mappings satisfying Φ-maps in S-metric spaces
- Author
-
Mohammad Rezaee, Stojan Radenovic, Shaban Sedghi, and Tatjana Došenović
- Subjects
Discrete mathematics ,General Mathematics ,010102 general mathematics ,common fixed point ,01 natural sciences ,010101 applied mathematics ,Metric space ,54h25 ,Common fixed point ,QA1-939 ,0101 mathematics ,s-metric space ,Coincidence point ,contractive maps ,47h10 ,Mathematics - Abstract
In this paper we prove the existence of the unique fixed point for the pair of weakly compatible self-mappings satisfying some Ф-type contractive conditions in the framework of S-metric spaces. Our results generalize, extend, unify, complement and enrich recently fixed point results in existing literature.
- Published
- 2016
46. Generalized pairing strategies-a bridge from pairing strategies to colorings
- Author
-
András Pluhár and Lajos Győrffy
- Subjects
k-in-a-row game ,positional games ,business.industry ,General Mathematics ,chooser-picker games ,0102 computer and information sciences ,02 engineering and technology ,Structural engineering ,01 natural sciences ,Bridge (interpersonal) ,pairing strategies ,010201 computation theory & mathematics ,hypergraph colorings ,Pairing ,05c15 ,0202 electrical engineering, electronic engineering, information engineering ,QA1-939 ,05c65 ,020201 artificial intelligence & image processing ,business ,Mathematics - Abstract
In this paper we define a bridge between pairings and colorings of the hypergraphs by introducing a generalization of pairs called t-cakes for t ∈ ℕ, t ≥ 2. For t = 2 the 2-cakes are the same as the well-known pairs of system of distinct representatives, that can be turned to pairing strategies in Maker-Breaker hypergraph games, see Hales and Jewett [12]. The two-colorings are the other extremity of t-cakes, in which the whole ground set of the hypergraph is one big cake that we divide into two parts (color classes). Starting from the pairings (2-cake placement) and two-colorings we define the generalized t-cake placements where we pair p elements by q elements (p, q ∈ ℕ, 1 ≤ p, q < t, p + q = t). The method also gives bounds on the condition of winnings in certain biased Chooser-Picker games, which can be introduced similarly to Beck [3]. We illustrate these ideas on the k-in-a-row games for different values of k on the infinite chessboard.
- Published
- 2016
47. The calculus of variations on jet bundles as a universal approach for a variational formulation of fundamental physical theories
- Author
-
Jana Musilová and Stanislav Hronek
- Subjects
General Mathematics ,symmetries ,010103 numerical & computational mathematics ,01 natural sciences ,Principle of least action ,variational physical theories ,Euler's laws of motion ,fibred manifolds ,symbols.namesake ,Analytical mechanics ,Laws of science ,Variational principle ,Calculus ,QA1-939 ,Hamilton's principle ,0101 mathematics ,[MATH]Mathematics [math] ,Mathematics ,010102 general mathematics ,calculus of variations ,Equations of motion ,equations of motion ,Classical mechanics ,Lagrangian mechanics ,symbols ,inverse problem ,conservation laws - Abstract
As widely accepted, justified by the historical developments of physics, the background for standard formulation of postulates of physical theories leading to equations of motion, or even the form of equations of motion themselves, come from empirical experience. Equations of motion are then a starting point for obtaining specific conservation laws, as, for example, the well-known conservation laws of momenta and mechanical energy in mechanics. On the other hand, there are numerous examples of physical laws or equations of motion which can be obtained from a certain variational principle as Euler-Lagrange equations and their solutions, meaning that the \true trajectories" of the physical systems represent stationary points of the corresponding functionals. It turns out that equations of motion in most of the fundamental theories of physics (as e.g. classical mechanics, mechanics of continuous media or fluids, electrodynamics, quantum mechanics, string theory, etc.), are Euler-Lagrange equations of an appropriately formulated variational principle. There are several well established geometrical theories providing a general description of variational problems of different kinds. One of the most universal and comprehensive is the calculus of variations on fibred manifolds and their jet prolongations. Among others, it includes a complete general solution of the so-called strong inverse variational problem allowing one not only to decide whether a concrete equation of motion can be obtained from a variational principle, but also to construct a corresponding variational functional. Moreover, conservation laws can be derived from symmetries of the Lagrangian defining this functional, or directly from symmetries of the equations. In this paper we apply the variational theory on jet bundles to tackle some fundamental problems of physics, namely the questions on existence of a Lagrangian and the problem of conservation laws. The aim is to demonstrate that the methods are universal, and easily applicable to distinct physical disciplines: from classical mechanics, through special relativity, waves, classical electrodynamics, to quantum mechanics.
- Published
- 2016
48. Ricci solitons on QR-hypersurfaces of a quaternionic space form ℚn
- Author
-
Z. Nazari and E. Abedi
- Subjects
Pure mathematics ,quaternionic space form ,General Mathematics ,010102 general mathematics ,Space form ,53c40 ,Mathematics::Spectral Theory ,01 natural sciences ,53c25 ,53c15 ,0103 physical sciences ,QA1-939 ,010307 mathematical physics ,Mathematics::Differential Geometry ,0101 mathematics ,Nonlinear Sciences::Pattern Formation and Solitons ,ricci soliton ,qr-hypersurfaces ,Mathematics - Abstract
The purpose of this paper is to study Ricci solitons on QR-hypersurfaces M of a quaternionic space form ℚn such that the shape operator A with respect to N has one eigenvalue. We prove that Ricci soliton on QR-hypersurfaces M with eigenvalue zero is steady and for eigenvalue nonzero is shrinking.
- Published
- 2016
49. On statistical convergence in quasi-metric spaces
- Author
-
Emrah Evren Kara and Merve İlkhan
- Subjects
40g15 ,General Mathematics ,010102 general mathematics ,quasi-metric space ,54e50 ,Statistical convergence ,01 natural sciences ,010101 applied mathematics ,Metric space ,forward and backward Cauchy sequences ,QA1-939 ,Natural density ,Applied mathematics ,statistical convergence ,p54a05 ,0101 mathematics ,Mathematics ,asymptotic density - Abstract
A quasi-metric is a distance function which satisfies the triangle inequality but is not symmetric in general. Quasi-metrics are a subject of comprehensive investigation both in pure and applied mathematics in areas such as in functional analysis, topology and computer science. The main purpose of this paper is to extend the convergence and Cauchy conditions in a quasi-metric space by using the notion of asymptotic density. Furthermore, some results obtained are related to completeness, compactness and precompactness in this setting using statistically Cauchy sequences.
- Published
- 2019
50. Some vector inequalities for two operators in Hilbert spaces with applications
- Author
-
Silvestru Sever Dragomir
- Subjects
Pure mathematics ,General Mathematics ,projection ,010103 numerical & computational mathematics ,01 natural sciences ,Combinatorics ,Inner product space ,symbols.namesake ,selfadjoint operators ,26d15 ,QA1-939 ,46c05 ,0101 mathematics ,Cauchy–Schwarz inequality ,Mathematics ,buzano’s inequality ,inner product spaces ,Triangle inequality ,schwarz’s inequality ,Nuclear operator ,010102 general mathematics ,Hilbert space ,Operator theory ,operator norm ,26d1 ,Bounded function ,unitary operators ,symbols ,Operator norm ,numerical radius - Abstract
In this paper we establish some vector inequalities for two operators related to Schwarz and Buzano results. We show amongst others that in a Hilbert space H we have the inequality 1 2 [ 〈 | A | 2 + | B | 2 2 x , x 〉 1 / 2 〈 | A | 2 + | B | 2 2 y , y 〉 1 / 2 + | 〈 | A | 2 + | B | 2 2 x , y 〉 | ] ≥ | 〈 Re ( B * A ) x , y 〉 | $${1 \over 2}\left[ {\left\langle {{{\left| {\rm{A}} \right|^2 + \left| {\rm{B}} \right|^2 } \over 2}{\rm{x}},{\rm{x}}} \right\rangle ^{1/2} \left\langle {{{\left| {\rm{A}} \right|^2 + \left| {\rm{B}} \right|^2 } \over 2}{\rm{y}},{\rm{y}}} \right\rangle ^{1/2} + \left| {\left\langle {{{\left| {\rm{A}} \right|^2 + \left| {\rm{B}} \right|^2 } \over {\rm{2}}}} {\rm{x}},{\rm{y}}\right\rangle } \right|} \right] \ge \left| {\left\langle {{\mathop{\rm Re}\nolimits} ({\rm{B}}*{\rm{A}})\,{\rm{x}},{\rm{y}}} \right\rangle } \right|$$ for A, B two bounded linear operators on H such that Re (B*A) is a nonnegative operator and any vectors x, y ∈ H. Applications for norm and numerical radius inequalities are given as well.
- Published
- 2016
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