Showing papers in "Filomat in 2018"
TL;DR: In this article, Zhu et al. introduced new soft separation axioms, namely p-soft Ti-spaces (i = 0, 1, 2, 3, 4), depending on a total non-belonging relation, and studied their features in detail.
Abstract: The main aim of the present paper is to define new soft separation axioms which lead us, first, to generalize existing comparable properties via general topology, second, to eliminate restrictions on the shape of soft open sets on soft regular spaces which given in [22], and third, to obtain a relationship between soft Hausdorff and new soft regular spaces similar to those exists via general topology. To this end, we define partial belong and total non belong relations, and investigate many properties related to these two relations. We then introduce new soft separation axioms, namely p-soft Ti-spaces (i = 0, 1, 2, 3, 4), depending on a total non belong relation, and study their features in detail. With the help of examples, we illustrate the relationships among these soft separation axioms and point out that p-soft Ti-spaces are stronger than soft Ti-spaces, for i = 0, 1, 4. Also, we define a p-soft regular space, which is weaker than a soft regular space and verify that a p-soft regular condition is sufficient for the equivalent among p-soft Ti-spaces, for i = 0, 1, 2. Furthermore, we prove the equivalent among finite p-soft Ti-spaces, for i = 1, 2, 3 and derive that a finite product of p-soft Ti-spaces is p-soft Ti, for i = 0, 1, 2, 3, 4. In the last section, we show the relationships which associate some p-soft Ti-spaces with soft compactness, and in particular, we conclude under what conditions a soft subset of a p-soft T2-space is soft compact and prove that every soft compact p-soft T2-space is soft T3-space. Finally, we illuminate that some findings obtained in general topology are not true concerning soft topological spaces which among of them a finite soft topological space need not be soft compact.
78 citations
TL;DR: In this article, a new three-step iteration process, called MINE, was proposed for approximation of fixed points in the setting of uniformly convex Banach spaces, and convergence results for Suzuki generalized nonexpansive mappings were proved.
Abstract: In this paper we propose a new three-step iteration process, called M
iteration process, for approximation of fixed points. Some weak and strong
convergence theorems are proved for Suzuki generalized nonexpansive mappings
in the setting of uniformly convex Banach spaces. Numerical example is given
to show the efficiency of new iteration process. Our results are the
extension, improvement and generalization of many known results in the
literature of iterations in fixed point theory.
65 citations
TL;DR: In this paper, the authors obtain sufficient conditions for the existence and uniqueness of point of coincidence by using simulation functions in the context of metric spaces and prove some interesting results, which generalize the corresponding results of [5, 8, 13, 14, 16] in several ways.
Abstract: In this paper, we obtain some sufficient conditions for the existence and
uniqueness of point of coincidence by using simulation functions in the
context of metric spaces and prove some interesting results. Our results
generalize the corresponding results of [5, 8, 13, 14, 16] in several
directions. Also, we provide an example which shows that our main result is
a proper generalization of the result of Jungck [American Math. Monthly
83(1976) 261-263], L-de-Hierro et al. [J. Comput. Appl. Math 275(2015)
345-355] and of Olgun et al. [Turk. J. Math. (2016) 40:832-837].
49 citations
TL;DR: In particular, limit representations of the core and dual core inverse are derived in this article, and corresponding limit representations for the dual core-EP inverse are also given in this paper.
Abstract: In this paper, we present three limit representations of the core-EP inverse. The first approach is based on the full-rank decomposition of a given matrix. The second and third approaches, which depend on the explicit expression of the core-EP inverse, are established. The corresponding limit representations of the dual core-EP inverse are also given. In particular, limit representations of the core and dual core inverse are derived
42 citations
TL;DR: In this paper, a new class of normalized bi-univalent functions in the open unit disk is defined by using a symmetric basic (or q-) derivative operator, and the estimates and inequalities involving the second Hankel determinant are investigated.
Abstract: In this paper, we discuss the various properties of a newly-constructed subclass of the class of normalized bi-univalent functions in the open unit disk, which is defined here by using a symmetric basic (or q-) derivative operator. Moreover, for functions belonging to this new basic (or q-) class of normalized biunivalent functions, we investigate the estimates and inequalities involving the second Hankel determinant.
38 citations
36 citations
TL;DR: In this article, the authors extend Ulam-Hyers stability to generalized generalized Caputo fractional differential equations with delay and dependence on a kernel function, and discuss the conditions that such generalized generalized CDFDEs should satisfy to be stable in the sense of Ulam Hrs and Ulam Rassias.
Abstract: The objective of this paper is to extend Ulam-Hyers stability and
Ulam-Hyers-Rassias stability theory to differential equations with delay and
in the frame of a certain class of a generalized Caputo fractional
derivative with dependence on a kernel function. We discuss the conditions
such delay generalized Caputo fractional differential equations should
satisfy to be stable in the sense of Ulam-Hyers and Ulam-Hyers-Rassias. To
demonstrate our results two examples are presented.
35 citations
TL;DR: In this article, by virtue of the Cauchy integral formula in the theory of complex functions, the authors established an integral representation for the generating function of the Catalan numbers in combinatorics.
Abstract: In the paper, by virtue of the Cauchy integral formula in the theory of
complex functions, the authors establish an integral representation for the
generating function of the Catalan numbers in combinatorics. From this, the
authors derive an alternative integral representation, complete
monotonicity, determinantal and product inequalities for the Catalan
numbers.
33 citations
TL;DR: In this paper, the properties of L-fuzzifying convergence spaces are investigated and it is shown that the category L-FYC is a strong topological universe and that L-FIFC is a subcategory of LFIFC.
Abstract: In this paper, categorical properties of L-fuzzifying convergence spaces are investigated. It is shown that (1) the category L-FYC of L-fuzzifying convergence spaces is a strong topological universe; (2) the category L-FYKC of L-fuzzifying Kent convergence spaces, as a bireflective and bicoreflective subcategory of L-FYC, is also a strong topological universe; (3) the category L-FYLC of L-fuzzifying limit spaces, as a bireflective subcategory of L-FYKC, is a topological universe.
31 citations
TL;DR: In this article, the Keller-Segel model with Atangana-Baleanu fractional derivative in CaputoINEINE sense was analyzed and the uniqueness of these solutions was examined.
Abstract: The new definition of the fractional derivative was defined by Atangana and
Baleanu in 2016. They used the generalized Mittag-Leffer function with the
non-singular and non-local kernel. Further, their version provides all
properties of fractional derivatives. Our aim is to analyse the Keller-Segel
model with Caputo and Atangana-Baleanu fractional derivative in Caputo
sense. Using fixed point theory, we first show the existence of coupled
solutions. We then examine the uniqueness of these solutions. Finally, we
compare our results numerically by modifying our model according to both
definitions, andwedemonstrate these results on the graphs in detail. All
computations were done using Mathematica.
27 citations
TL;DR: In this paper, two new general subclasses HΣm(τ, γ;α) and Hðm(γ, β; β) of Σm consisting of analytic and m-fold symmetric bi-univalent functions were introduced.
Abstract: In the present investigation, we consider two new general subclasses HΣm(τ, γ;α) and HΣm(τ, γ;β) of Σm consisting of analytic and m-fold symmetric bi-univalent functions in the open unit disk U. For functions belonging to the two classes introduced here, we derive estimates on the initial coefficients |am+1| and |a2m+1|. Several related classes are also considered and connections to earlier known results are made. 2010 Mathematics Subject Classification: 30C45, 30C50, 30C80.
TL;DR: In this article, the existence of critical points for the energy functional which is unbounded below and satisfies the Palais-Smale condition is proved for a singular elliptic problem involving p(x)−Laplacian operator in a bounded domain in RN.
Abstract: Here, a singular elliptic problem involving p(x)−Laplacian operator in a bounded domain in RN is considered. Due to this, the existence of critical points for the energy functional which is unbounded below and satisfies the Palais-Smale condition are proved.
TL;DR: In this paper, Mohiuddine et al. proved a Korovkin type approximation theorem for the set of functions defined on a Banach space and demonstrated that their theorem is a non-trivial extension of some well-known k-means.
Abstract: Statistical (C,1) summability and a Korovkin type approximation theorem has
been proved by Mohiuddine et al. [20] (see [S. A. Mohiuddine, A. Alotaibi
and M. Mursaleen, Statistical summability (C,1) and a Korovkin type
approximation theorem, J. Inequal. Appl. 2012 (2012), Article ID 172, 1-8).
In this paper, we apply statistical deferred Cesaro summability method to
prove a Korovkin type approximation theorem for the set of functions 1, e-x
and e-2x defined on a Banach space C[0;1) and demonstrate that our theorem
is a non-trivial extension of some well-known Korovkin type approximation
theorems. We also establish a result for the rate of statistical deferred
Cesaro summability method. Some interesting examples are also discussed
here in support of our definitions and results.
TL;DR: In this paper, new conditions on the entire coefficients A(z) and B(z), which guarantee that every nontrivial solution of f''+A(z)) f'+B(z') f = 0 is of infinite order, are given.
Abstract: Some new conditions on the entire coefficients A(z) and B(z), which guarantee
every nontrivial solution of f''+A(z) f'+B(z) f = 0 is of infinite
order, are given in this paper. Two classes of entire functions are involved
in these conditions, the one is entire functions having Fabry gaps, the
another is function extremal for Yang’s inequality. Moreover, a kind of
entire function having finite Borel exception value is considered.
TL;DR: In this article, a multi-variable conformable fractional derivative for a vector valued function with several variables is introduced, which is based on Khalil et al.'s concept.
Abstract: Conformable fractional derivative is introduced by the authors Khalil et al. In this study we
develop their concept and introduce multi-variable conformable derivative for a vector valued function
with several variables
TL;DR: In this paper, a number of refinements inequalities for the Hermite$-$Hadamard's type inequality and the trapezoid inequalities were investigated in terms of a generalized fractional integral operator and a considerable amount of results for special means.
Abstract: By using contemporary theory of inequalities, this study is devoted topropose a number of refinements inequalities for the Hermite$-$Hadamard'stype inequality and conclude explicit bounds for the trapezoid inequalitiesin terms of $s$-convex mappings, at most second derivative through theinstrument of generalized fractional integral operator and a considerableamount of results for special means The results of this study which are thegeneralization of those given in earlier works are obtained for functions $f$where $|f^{\prime }|$ and $|f^{\prime \prime }|$ (or $|f^{\prime }|^{q}$ and $|f^{\prime \prime }|^{q}$ for $q\geq 1$) are $s$-convex hold by applyingthe Holder inequality and the power mean inequality
TL;DR: In this article, it was shown that there exists a class of warped product submanifolds of a Kaehler manifold such that the spherical manifold of the warped product is pointwise slant.
Abstract: It was shown in [15, 16] that there does not exist any warped product submanifold of a Kaehler manifold such that the spherical manifold of the warped product is proper slant. In this paper, we introduce the notion of warped product submanifolds with a slant function. We show that there exists a class of nontrivial warped product submanifolds of a Kaehler manifold such that the spherical manifold is pointwise slant by giving an example and a characterization theorem. We also prove that if the warped product is mixed totally geodesic then the warping function is constant.
TL;DR: In this paper, the existence of infinitely many solutions is proved by variational methods in Sobolev spaces and the critical points principle of Ricceri, where the exponent in the singular term is different from that in the p-biharmonic operator.
Abstract: Here, a fourth order singular elliptic problem involving p-biharmonic operator with Dirichlet boundary condition is established where the exponent in the singular term is different from that in the p-biharmonic operator. The existence of infinitely many solutions is proved by the variational methods in Sobolev spaces and the critical points principle of Ricceri. Finally, an example is presented.
TL;DR: The attribute weights under different time sequence based on intuitionistic fuzzy entropy minimization are determined and the optimal scheme that is closet to ideal solution is obtained.
Abstract: According to the decision information of multi-attribute decision-making problem with fuzzy and temporal characteristics, a dynamic intuitionistic fuzzy decision making method based on time preference and VIKOR is proposed. First, we determined the attribute weights under different time sequence based on intuitionistic fuzzy entropy minimization; secondly, we introduced the time degree function reflecting the decision makers’ subjective time preference, and established a multi-objective programming model to obtain time weights; then we used dynamic intuitionistic fuzzy weighted geometric (DIFWG) operator to integrate different time periods of the intuitionistic fuzzy decision matrices; the VIKOR method is used in ranking solutions that takes account of group effectiveness maximization and individual regret minimization, and obtained the optimal scheme that is closet to ideal solution; finally, the feasibility and effectiveness of the proposed method is verified by the example of a technology innovation alliance partner selection.
TL;DR: In this article, the generalized Drazin inverse of a (2,2,0) block matrix over a Banach algebra under certain circumstances was derived, which generalizes and unifies several results in the literature.
Abstract: In this paper, we give expressions for the generalized Drazin inverse of a (2,2,0) block matrix over a Banach algebra under certain circumstances, utilizing which we derive the generalized Drazin inverse of a 2× 2 block matrix in a Banach algebra under weaker restrictions. Our results generalize and unify several results in the literature.
TL;DR: In this paper, contraction mappings of Meir-Keeler types on modular metric spaces were introduced and the existence and uniqueness of their fixed points were investigated, and the authors gave an example which demonstrates their theoretical results.
Abstract: In this paper we introduce contraction mappings of Meir-Keeler types on modular metric spaces and investigate the existence and uniqueness of their fixed points. We give an example which demonstrates our theoretical results.
TL;DR: In this paper, the authors characterize the map δ when U is a zero product determined algebra and apply it to properly infinite W?-algebras and unital simple C?-algesas with a non-trivial idempotent.
Abstract: Let U be a unital ?-algebra and δ : U → U be a linear map behaving like a derivation or an anti-derivation at the following orthogonality conditions on elements of U: xy = 0, xy? = 0, xy = yx = 0 and xy? = y?x = 0. We characterize the map δ when U is a zero product determined algebra. Special characterizations are obtained when our results are applied to properly infinite W?-algebras and unital simple C?-algebras with a non-trivial idempotent.
TL;DR: In this paper, the properties of the Nörlund and Riesz mean of complex uncertain variables were investigated and the results on oscillating sequences of complex uncertainty variables were proved.
Abstract: In this article we have investigated some properties of the Nörlund and Riesz mean of sequences of complex uncertain variables. Also, we prove results on oscillating sequences of complex uncertain variables.
Abstract: Recently, B.-Y. Chen and O.J. Garay studied pointwise slant submanifolds of almost Hermitian manifolds. In this paper, first we study pointwise slant and pointwise pseudo-slant submanifolds of almost contact metric manifolds and then using this notion, we show that there exist a non-trivial class of warped product pointwise pseudo-slant submanifolds of Sasakian manifolds by giving some useful results, including a characterization.
TL;DR: In this paper, the existence of a fixed point is investigated in the setting of extended b-metric spaces and a fixed-point theorem is presented. But the existence is not proved in the sense of the contraction conditions and in the frame of abstract spaces.
Abstract: In this paper, we introduce a notion of (α,ψ)-K-contraction in the setting of extended b-metric spaces and investigate the existence of a fixed point. The presented results generalize and unify a number of well-known fixed point theorem mainly in two distinct aspects; in the sense of the contraction conditions and in the frame of abstract spaces.
TL;DR: In this paper, a discontinuous boundary value problem with piecewise continuous potential was investigated, and it was shown that the generalized eigenvectors form a RieszINE basis of the adequate Hilbert space, and that the problem under consideration has precisely denumerable many eigenvalues λ 1, λ 2,..., which are real and tend to + ∞.
Abstract: We investigate a discontinuous boundary value problem which consists of a
Sturm-Liouville equation with piecewise continuous potential together with
eigenparameter dependent boundary conditions and supplementary transmission
conditions. We establish some spectral properties of the considered problem.
In particular, it is shown that the problem under consideration has
precisely denumerable many eigenvalues λ1, λ2,..., which are real and tends
to +∞. Moreover, it is proven that the generalized eigenvectors form a Riesz
basis of the adequate Hilbert space.
TL;DR: In this article, Wang et al. investigated *-DMP elements in $*$-semigroups and $ *$-rings and gave necessary and sufficient conditions for two elements $a,~b$ in $ *-rings to have $aa^{\scriptsize\textcircled{\tiny D}}=bb^{1,3\}-inverse, Drazin inverse and pseudo core inverse, respectively.
Abstract: In this paper, we investigate *-DMP elements in $*$-semigroups and $*$-rings. The notion of *-DMP element was introduced by Patr\'{i}cio in 2004. An element $a$ is *-DMP if there exists a positive integer $m$ such that $a^{m}$ is EP. We first characterize *-DMP elements in terms of the \{1,3\}-inverse, Drazin inverse and pseudo core inverse, respectively.
Then, we give the pseudo core decomposition utilizing the pseudo core inverse, which extends the core-EP decomposition introduced by Wang for matrices to an arbitrary $*$-ring; and this decomposition turns to be a useful tool to characterize *-DMP elements. Further, we extend Wang's core-EP order from matrices to $*$-rings and use it to investigate *-DMP elements. Finally, we give necessary and sufficient conditions for two elements $a,~b$ in $*$-rings to have $aa^{\scriptsize\textcircled{\tiny D}}=bb^{\scriptsize\textcircled{\tiny D}}$, which contribute to investigate *-DMP elements.
TL;DR: This paper constructs a multi-bijective linguistic soft decision system by employing the matrices corresponding to the bijective soft sets generated from the linguistic variable parameters.
Abstract: In this paper, we firstly introduce bijective soft matrix theory and research its operations, properties and algebraic structures in detail. Also, we present a bijective soft decision system based on the bijective soft matrix theory. Moreover, we construct a multi-bijective linguistic soft decision system by employing the matrices corresponding to the bijective soft sets generated from the linguistic variable parameters. Finally, the system’s decision algorithm and its application for a decision making problem are given. By using the algorithm, we determine both the linguistic variables according to the parameters and the parameters affecting the optimal choice according to the highest linguistic decision value.
TL;DR: In this article, a bivariate extension of Schurer-Stancu operators based on (p,q)-integers is introduced, and the authors prove uniform convergence rate and degree of approximation by means of Bohman-Korovkin type theorem.
Abstract: The aim of this article is to introduce a bivariate extension of
Schurer-Stancu operators based on (p,q)-integers. We prove uniform
approximation by means of Bohman-Korovkin type theorem, rate of convergence
using total modulus of smoothness and degree of approximation via second
order modulus of smoothness, Peetre’s K-functional, Lipschitz type class.
TL;DR: In this paper, two inequalities in the geometry of gradient Ricci solitons on a smooth manifold were discussed, which provide some relationships between the curvature of the Riemannian metric and the behavior of the scalar field.
Abstract: This short note concerns with two inequalities in the geometry of gradient Ricci solitons $(g, f, \lambda )$ on a smooth manifold $M$. These inequalities provide some relationships between the curvature of the Riemannian metric $g$ and the behavior of the scalar field $f$ through two second order equations satisfied by the scalar $\lambda $. We propose several generalizations of Ricci solitons to the setting of manifolds endowed with linear connections, not necessary of metric type.