Showing papers in "Turkish Journal of Mathematics in 2021"
TL;DR: In this paper, the existence and uniqueness criteria for a new coupled Caputo conformable system of pantograph problems were explored, in which the given boundary conditions were formulated in the Riemann-Liouville conformable framework.
Abstract: Our fundamental purpose in the present manuscript is to explore existence and uniqueness criteria for a new coupled Caputo conformable system of pantograph problems in which for the first time, the given boundary conditions are formulated in the Riemann–Liouville conformable framework. To reach the mentioned aims, we utilize different analytical techniques in which some fixed point results play a vital role. In the final part, a simulative example is designed to cover the applicability aspects of theoretical findings available in this research manuscript from a numerical point of view.
74 citations
TL;DR: The main contribution of the present article is to introduce a modification and a generalization for Feng's approximations, namely, soft β -rough approxIMations, and some of their properties will be studied.
Abstract: Soft rough set theory has been presented as a basic mathematical model for decision-making for many real-life data However, soft rough sets are based on a possible fusion of rough sets and soft sets which were proposed by Feng et al [20] The main contribution of the present article is to introduce a modification and a generalization for Feng's approximations, namely, soft β -rough approximations, and some of their properties will be studied A comparison between the suggested approximations and the previous one [20] will be discussed Some examples are prepared to display the validness of these proposals Finally, we put an actual example of the infections of coronavirus (COVID-19) based on soft β -rough sets This application aims to know the persons most likely to be infected with COVID-19 via soft β -rough approximations and soft β -rough topologies [ABSTRACT FROM AUTHOR] Copyright of Turkish Journal of Mathematics is the property of Scientific and Technical Research Council of Turkey and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission However, users may print, download, or email articles for individual use This abstract may be abridged No warranty is given about the accuracy of the copy Users should refer to the original published version of the material for the full abstract (Copyright applies to all Abstracts )
27 citations
TL;DR: In this paper, the authors considered a kind of nonlinear Nabla Caputo fractional difference system with variable order and fixed initial valuable and gave sufficient conditions to guarantee the existence results for the considered fractional discrete equations.
Abstract: This paper is concerned with a kind of nonlinear Nabla Caputo fractional difference system with variableorder and fixed initial valuable. By applying Krasnoselskii’s fixed point theorem, we give some sufficient conditions to guarantee the existence results for the considered fractional discrete equations. In addition, we further consider the Ulam-Hyers stability by means of generalized Gronwall inequality. At last, two typical examples are delineated to demonstrate the effectiveness of our theoretical results.
16 citations
15 citations
13 citations
TL;DR: In this article, the authors compute sub-Riemannian limits of Gaussian curvature for a C -smooth surface in the Lorentzian Heisenberg group for the second and the third Gaussian metric.
Abstract: In this paper, we compute sub-Riemannian limits of Gaussian curvature for a C -smooth surface in the Lorentzian Heisenberg group for the second Lorentzian metric and the third Lorentzian metric and signed geodesic curvature for C -smooth curves on surfaces. We get Gauss–Bonnet theorems in the Lorentzian Heisenberg group for the second Lorentzian metric and the third Lorentzian metric.
12 citations
TL;DR: In this paper, the authors developed scattering and spectral analysis of a discrete impulsive Sturm-Liouville equation with spectral parameter in boundary condition, and gave the Jost solution and scattering solutions of this problem.
Abstract: This work develops scattering and spectral analysis of a discrete impulsive Sturm–Liouville equation with spectral parameter in boundary condition. Giving the Jost solution and scattering solutions of this problem, we find scattering function of the problem. Discussing the properties of scattering function, scattering solutions, and asymptotic behavior of the Jost solution, we find the Green function, resolvent operator, continuous and point spectrum of the problem. Finally, we give an example in which the main results are made explicit.
10 citations
TL;DR: In this paper, a new matrix called quasi-Cesàro matrix is proposed, which is a generalization of the ordinary Cesàro matrices and introduces BK -spaces C k and C q ∞ as the domain of the quasi-cesàros matrix C in the spaces lk and l∞, respectively.
Abstract: In the present study, we construct a new matrix which we call quasi-Cesàro matrix and is a generalization of the ordinary Cesàro matrix, and introduce BK -spaces C k and C q ∞ as the domain of the quasi-Cesàro matrix C in the spaces lk and l∞, respectively. Furthermore, we exhibit some topological properties and inclusion relations related to these newly defined spaces. We determine the basis of the space C k and obtain Köthe duals of the spaces C q k and C q ∞. Based on the newly defined matrix, we present a factorization for the Hilbert matrix and generalize Hardy’s inequality, as an application. Moreover we find the norm of this new matrix as an operator on several matrix domains.
9 citations
TL;DR: In this article, the nabla unification of the discrete and continuous Hardy-Copson type inequalities was studied for the discrete, continuous, and delta cases, and some of the obtained inequalities are nabla counterparts of their delta versions.
Abstract: Abstract: This paper is devoted to the nabla unification of the discrete and continuous Hardy–Copson type inequalities. Some of the obtained inequalities are nabla counterparts of their delta versions while the others are new even for the discrete, continuous, and delta cases. Moreover, these dynamic inequalities not only generalize and unify the related ones in the literature but also improve them in the special cases.
9 citations
9 citations
TL;DR: In this paper, a class of analytic functions F(β,λ) (H,α, δ, μ) satisfying the following subordinate condition associated with Chebyshev polynomials was defined.
Abstract: In this paper,we define a class of analytic functions F(β,λ) (H,α, δ, μ) , satisfying the following subordinate condition associated with Chebyshev polynomials α [ zG ′ (z) G (z) ]δ + (1− α) [ zG ′ (z) G (z) ]μ [ 1 + zG ′′ (z) G (z) 1−μ ≺ H (z, t) , where G (z) = λβzf ′′ (z) + (λ− β) zf ′ (z) + (1− λ+ β) f (z) , 0 ≤ α ≤ 1, 1 ≤ δ ≤ 2, 0 ≤ μ ≤ 1, 0 ≤ β ≤ λ ≤ 1 and t ∈ ( 1 2 , 1 ] . We obtain initial coefficients |a2| and |a3| for this subclass by means of Chebyshev polynomials expansions of analytic functions in D. Furthermore, we solve Fekete-Szegö problem for functions in this subclass.We also provide relevant connections of our results with those considered in earlier investigations. The results presented in this paper improve the earlier investigations.
TL;DR: In this paper, the concept of neutrosophic soft continuous mapping and its properties have been introduced along with the investigation of their several characteristics, and verified by proper examples, along with their properties and properties.
Abstract: In this paper, the concept of neutrosophic soft continuous mapping, neutrosophic soft open mapping, neutrosophic soft closed mapping and neutrosophic soft homeomorphism have been introduced along with the investigation of their several characteristics, and verified by proper examples.
TL;DR: In this paper, the authors characterize closed and strongly closed subsets of convergence approach spaces and introduce two notions of closure in the category of convergent approach spaces which satisfy idempotent, productive and (weakly) hereditary properties.
Abstract: In this paper, we characterize closed and strongly closed subsets of convergence approach spaces and introduce two notions of closure in the category of convergence approach spaces which satisfy idempotent, productive and (weakly) hereditary properties. Furthermore, we explicitly characterize each of Ti convergence approach spaces, i = 0, 1, 2 with respect to these closure operators and show that each of these subcategories of Ti convergence approach spaces, i = 0, 1, 2 are epireflective as well as we investigate the relationship among these subcategories. Finally, we characterize connected convergence approach spaces.
TL;DR: In this article, a novel Φ -fractional Bielecki-type norm was used to obtain results on uniqueness and Ulam stability of solutions for a new class of multiterms fractional differential equations in the framework of generalized Caputo fractional derivative.
Abstract: In this research article, a novel Φ -fractional Bielecki-type norm introduced by Sousa and Oliveira [23] is used to obtain results on uniqueness and Ulam stability of solutions for a new class of multiterms fractional differential equations in the framework of generalized Caputo fractional derivative. The uniqueness results are obtained by employing Banach’ and Perov’s fixed point theorems. While the Φ -fractional Gronwall type inequality and the concept of the matrices converging to zero are implemented to examine different types of stabilities in the sense of Ulam–Hyers (UH) of the given problems. Finally, two illustrative examples are provided to demonstrate the validity of our theoretical findings.
TL;DR: In this paper, the authors used the triangular A−statistical convergence for double sequences, which is an interesting convergence method, and proved a Korovkin-type approximation theorem for positive linear operators on the space of all real-valued continuous functions on [0,∞)× [0 ∞] with the property that have a finite limit at the infinity.
Abstract: In the present paper, using the triangular A−statistical convergence for double sequences, which is an interesting convergence method, we prove a Korovkin-type approximation theorem for positive linear operators on the space of all real-valued continuous functions on [0,∞)× [0,∞) with the property that have a finite limit at the infinity. Moreover, we present the rate of convergence via modulus of continuity. Finally, we give some further developments.
TL;DR: In this paper, the structural properties of k-quasi-m -symmetric operators are established with the help of operator matrix representation, and generalized Weyl's theorem holds for k-squasi-3 -symmetric operators.
Abstract: m -symmetric operator plays a crucial role in the development of operator theory and has been widely studied due to unexpected intimate connections with differential equations, particularly conjugate point theory and disconjugacy. For positive integers m and k , an operator T is said to be a k -quasi-m -symmetric operator if T ∗k( m ∑ j=0 (−1)(j )T ∗m−jT )T k = 0 , which is a generalization of m -symmetric operator. In this paper, some basic structural properties of k -quasi-m -symmetric operators are established with the help of operator matrix representation. In particular, we also show that every k -quasi-3 -symmetric operator has a scalar extension. Finally, we prove that generalized Weyl’s theorem holds for k -quasi-3 -symmetric operators.
TL;DR: In this article, the authors introduced the nearness near-ring, sub-nearness nearring, nearness M-group, and nearness ideal structures for the set of all near left weak cosets.
Abstract: In this study, nearness near-ring, subnearness near-ring, nearness M-group and nearness ideal are introduced. By considering operations on the set of all near left weak cosets, nearness near-ring of all near left weak cosets and nearness near-ring homomorphism are also presented. Moreover, some properties of these structures are investigated.
TL;DR: In this paper, the cardinality and rank of the subsemigroup N(Cn,r) of Cn under its natural order was studied, and it was shown that the set Nr(cn, r) is a sub-semigroup of the set of all n-potent elements of Nn.
Abstract: Let Cn be the semigroup of all order-preserving and decreasing transformations on X = {1, . . . , n} under its natural order, and let N(Cn) be the subsemigroup of all nilpotent elements of Cn . For 1 ≤ r ≤ n− 1 , let N(Cn,r) = {α ∈ N(Cn) : |im (α)| ≤ r}, Nr(Cn) = {α ∈ N(Cn) : α is an m-potent for any 1 ≤ m ≤ r}. In this paper we find the cardinality and the rank of the subsemigroup N(Cn,r) of Cn . Moreover, we show that the set Nr(Cn) is a subsemigroup of N(Cn) and then, we find a lower bound for the rank of Nr(Cn) .
TL;DR: In this paper, a ring R is JN if its Jacobson radical coincides with upper nilradical, and R is right SR if each element r ∈ R can be written as r = s+r where s is an element from the right socle and r is a regular element of R.
Abstract: We call a ring R is JN if whose Jacobson radical coincides with upper nilradical, and R is right SR if each element r ∈ R can be written as r = s+r where s is an element from the right socle and r is a regular element of R . SR rings is a class of special subrings of JN rings, which is the extension of soclean rings. We give their some characterizations and examples, and investigate the relationship between JN rings, SR rings and related rings, respectively.
TL;DR: In this paper, a function f ∈ H(D) belongs to the Hardy space H if f < p < ∞ and f belongs to Zygmund type space Z.
Abstract: See for example [1, 9, 10]. Let α > 0 . Then W (1−|z|2)α = B (Bloch type space), W (2) (1−|z|2)α = Z α (Zygmund type space) and W (1−|z|2) log 2 1−|z|2 coincides with the logarithmic Bloch space Blog . Also W μ = Hμ (weighted type space), W μ = Bμ(weighted Bloch space) and W μ = Zμ (weighted Zygmund space). For more information about Bloch type spaces or Zygmund type spaces see [8, 15, 16]. For 0 < p < ∞ a function f ∈ H(D) belong to the Hardy space H if
TL;DR: In this article, a ternary version of hom-lie bialgebras, 3-Hom-Lie Bialgebases, is introduced and studied, and some key constructions and 3-dimensional classification are provided.
Abstract: The purpose of this paper is to introduce and study 3 -Hom-Lie bialgebras, which are a ternary version of HomLie bialgebras introduced by Yau (2015). We provide their properties, some key constructions and their 3 -dimensional classification. Moreover we discuss their representation theory and their generalized derivations and coderivations. Furthermore, a more generalized notion called generalized 3 -Hom-Lie bialgebra is also considered.
TL;DR: In this article, the authors studied conformal generic submersions from almost Hermitian manifolds and obtained some properties, including the integrability of distributions, the geometry of foliations and totally geodesic foliations.
Abstract: Akyol and Şahin (2017) introduced the notion of conformal semiinvariant submersions from almost Hermitian manifolds. The present paper deals with the study of conformal generic submersions from almost Hermitian manifolds which extends semiinvariant Riemannian submersions, generic Riemannian submersions and conformal semiinvariant submersions in a natural way. We mention some examples of such maps and obtain characterizations and investigate some properties, including the integrability of distributions, the geometry of foliations and totally geodesic foliations. Moreover, we obtain some conditions for such submersions to be totally geodesic and harmonic, respectively.
TL;DR: In this paper, the authors investigate properties of order compact, unbounded order compact and relatively uniformly compact operators acting on vector lattices, and derive new results related to these classes of operators.
Abstract: We investigate properties of order compact, unbounded order compact and relatively uniformly compact operators acting on vector lattices. An operator is said to be order compact if it maps an arbitrary order bounded net to a net with an order convergent subnet. Analogously, an operator is said to be unbounded order compact if it maps an arbitrary order bounded net to a net with uo -convergent subnet. After exposing the relationships between order compact, unbounded order compact, semicompact and GAM -compact operators; we study those operators mapping an arbitrary order bounded net to a net with a relatively uniformly convergent subnet. By using the nontopological concepts of order and unbounded order convergences, we derive new results related to these classes of operators.
TL;DR: In this paper, two subclasses B(p, q, α, β, β) and B1(p and Jn,p) of p-valently Bazilević functions defined by higher order derivatives are studied.
Abstract: In this paper we consider two subclasses B(p, q, α, β) and B1(p, q, α, β) of p-valently Bazilević functions defined by higher order derivatives, and we defined and studied some properties of the images of the functions of these classes by the integral operators In,p and Jn,p for multivalent functions, defined by using higher order derivatives.
TL;DR: In this article, a generalized gamma function and two generalized beta functions in several variables are introduced and their properties are discussed, among others, recurrence relationships, Mellin transform properties, and partial differential equations involving these generalized functions.
Abstract: Abstract: Intensive studies aiming to extend the gamma and beta functions and to establish some properties for these extensions have been recently carried out. In this paper, we first introduce a generalized gamma function in n variables. Afterwards, two generalized beta functions in several variables are introduced and their properties are discussed. Among others, we investigate recurrence relationships, Mellin transform properties, and partial differential equations involving these generalized functions. At the end, some results about partial derivatives of these extended functions are presented as well.
TL;DR: In this article, the necessary and sufficient condition for a second-order weakly subdifferentiable function to have a global minimum has been proved, and it has been shown that such a function is both lower semicontinuous and lower Lipschitz.
Abstract: This article deals with second-order weak subdifferential. Firstly, the concept of second-order weak subdifferential is defined. Next, some of its properties are investigated. The necessary and sufficient condition for a second-order weakly subdifferentiable function to have a global minimum has been proved. It has been proved that a second-order weakly subdifferentiable function is both lower semicontinuous and lower Lipschitz.