Showing papers in "Fixed Point Theory and Applications in 2017"
TL;DR: In this article, the authors introduce a new class of admissible mappings and provide some fixed point theorems involving this class of mappings satisfying new conditions of contractivity in the setting of b-metric-like spaces.
Abstract: In this paper, we introduce a new class of α
q
s
p
$\alpha_{qs^{p}}$
-admissible mappings and provide some fixed point theorems involving this class of mappings satisfying some new conditions of contractivity in the setting of b-metric-like spaces. Our results extend, unify, and generalize classical and recent fixed point results for contractive mappings.
18 citations
TL;DR: In this article, the authors obtained generalizations of fixed point results for Kannan, Chatterjea and Hardy-Rogers contraction mappings in a new class of generalized metric spaces introduced by Jleli and Samet.
Abstract: In this paper, we obtain some generalizations of fixed point results for Kannan, Chatterjea and Hardy-Rogers contraction mappings in a new class of generalized metric spaces introduced recently by Jleli and Samet (Fixed Point Theory Appl. 2015:33, 2015).
15 citations
TL;DR: In this paper, a generalization of metric space over a Banach algebra is introduced and some fixed point theorems are proved in this space and proper examples are provided to establish the validity and superiority of their results.
Abstract: Rectangular cone b-metric spaces over a Banach algebra are introduced as a generalization of metric space and many of its generalizations. Some fixed point theorems are proved in this space and proper examples are provided to establish the validity and superiority of our results. An application to solution of linear equations is given which illustrates the proper application of the results in spaces over Banach algebra.
12 citations
TL;DR: In this paper, some nonunique fixed results in the setting of various abstract spaces are proposed. The proposed results extend, generalize and unify many existing results in corresponding literature.
Abstract: In this paper, we suggest some nonunique fixed results in the setting of various abstract spaces. The proposed results extend, generalize and unify many existing results in the corresponding literature.
11 citations
TL;DR: In this article, the authors apply the topological degree theory for condensing maps to study approximation of solutions to a fractional-order semilinear differential equation in a Banach space.
Abstract: We apply the topological degree theory for condensing maps to study approximation of solutions to a fractional-order semilinear differential equation in a Banach space. We assume that the linear part of the equation is a closed unbounded generator of a C
0
$C_{0}$
-semigroup. We also suppose that the nonlinearity satisfies a regularity condition expressed in terms of the Hausdorff measure of noncompactness. We justify the scheme of semidiscretization of the Cauchy problem for a differential equation of a given type and evaluate the topological index of the solution set. This makes it possible to obtain a result on the approximation of solutions to the problem.
10 citations
TL;DR: In this article, the existence of solutions for systems of random semilinear impulsive differential equations was established by means of a new version of Perov's, a nonlinear alternative of Leray-Schauder's fixed point principles combined with a technique based on vector-valued metrics and convergent to zero matrices.
Abstract: In this paper, we study the existence of solutions for systems of random semilinear impulsive differential equations. The existence results are established by means of a new version of Perov’s, a nonlinear alternative of Leray-Schauder’s fixed point principles combined with a technique based on vector-valued metrics and convergent to zero matrices. Also, we give a random abstract formulation to Sadovskii’s fixed point theorem in a vector-valued Banach space. Examples illustrating the results are included.
9 citations
TL;DR: In this paper, the completeness of a ν-generalized metric space has been studied and Caristi's and Subrahmanyam's fixed point theorems in the space have been improved.
Abstract: We extend Nadler’s fixed point theorem to ν-generalized metric spaces. Through the proof of the above extension, we understand more deeply the mathematical structure of a ν-generalized metric space. In particular, we study the completeness of the space. We also improve Caristi’s and Subrahmanyam’s fixed point theorems in the space.
7 citations
TL;DR: Czerwik as mentioned in this paper gave the probabilistic aspect to the known b-metric spaces, which leads to studying the fixed point property for nonlinear contractions in this new class of spaces.
Abstract: This work is for giving the probabilistic aspect to the known b-metric spaces (Czerwik in Atti Semin. Mat. Fis. Univ. Modena 46(2):263-276, 1998), which leads to studying the fixed point property for nonlinear contractions in this new class of spaces.
7 citations
TL;DR: In this paper, the authors search for best proximity point results for a novel class of non-self-mappings, called generalized proximal α-β-quasi-contractive.
Abstract: Herein, we search for some best proximity point results for a novel class of non-self-mappings $T:A \longrightarrow B$
called generalized proximal α-β-quasi-contractive. We illustrate our work by an example. Our results generalize and extend many recent results appearing in the literature. Several consequences are derived. As applications, we explore the existence of best proximity points for a metric space endowed with symmetric binary relation.
6 citations
TL;DR: In this article, the existence of a common best proximity point for a pair of multivalued non-self mappings in partially ordered metric spaces is proved. But it is not known whether such a point exists for all mappings.
Abstract: In this paper, we prove the existence of a common best proximity point for a pair of multivalued non-self mappings in partially ordered metric spaces. Also, we provide some interesting examples to illustrate our main results.
4 citations
TL;DR: In this paper, the authors present several coincidence type results for morphisms in the sense of Gorniewicz and Granas, in which the morphisms are assumed to be Gaussian.
Abstract: In this paper we present several coincidence type results for morphisms (fractions) in the sense of Gorniewicz and Granas.
TL;DR: In this paper, a dislocated cone metric space over Banach algebra is introduced as a generalisation of a cone metric spaces over the Banach Algebra and is used to prove fixed point theorems for Perov-type α-quasi contraction mapping, Kannan-type contraction mapping and Chatterjee-style contraction mapping.
Abstract: A dislocated cone metric space over Banach algebra is introduced as a generalisation of a cone metric space over Banach algebra as well as a dislocated metric space. Fixed point theorems for Perov-type α-quasi contraction mapping, Kannan-type contraction as well as Chatterjee-type contraction mappings are proved in a dislocated cone metric space over Banach algebra. Proper examples are provided to establish the validity of our claims.
TL;DR: In this article, the authors obtained a unique common coupled fixed point theorem by using $(\psi, \alpha, \beta )$ -contraction in ordered partial metric spaces.
Abstract: In this paper, we obtain a unique common coupled fixed point theorem by using $(\psi , \alpha , \beta )$
-contraction in ordered partial metric spaces. We give an application to integral equations as well as homotopy theory. Also we furnish an example which supports our theorem.
TL;DR: In this article, the concept of C-class functions is used to establish the best proximity point results for a certain class of proximal contractive mappings in S-metric spaces.
Abstract: In this paper, we use the concept of C-class functions to establish the best proximity point results for a certain class of proximal contractive mappings in S-metric spaces. Our results extend and improve some known results in the literature. We give examples to analyze and support our main results.
TL;DR: In this article, the authors define a homotopy for fuzzy spaces and show that the property of having a fixed point is invariant by the homophotonicity of a fuzzy space.
Abstract: The first purpose of this paper is to define a homotopy for fuzzy spaces. We continue our work by showing that the property of having a fixed point is invariant by this homotopy. These theorems generalize and improve well-known results.
TL;DR: In this paper, a Krasnoselskii-type and a Halpern-type algorithm for approximating a common fixed point of a countable family of totally quasi-asymptotically nonexpansive nonself multi-valued maps and a solution of a system of generalized mixed equilibrium problem are constructed.
Abstract: In this article, a Krasnoselskii-type and a Halpern-type algorithm for approximating a common fixed point of a countable family of totally quasi-ϕ-asymptotically nonexpansive nonself multi-valued maps and a solution of a system of generalized mixed equilibrium problem are constructed. Strong convergence of the sequences generated by these algorithms is proved in uniformly smooth and strictly convex real Banach spaces with the Kadec-Klee property. Several applications of our theorems are also presented. Finally, our theorems are a significant improvement of several important recent results.
TL;DR: In this article, the authors give characterizations of the contractive conditions, by using convergent sequences, and discuss the contractively defined conditions of integral type by using a unified method.
Abstract: We give characterizations of the contractive conditions, by using convergent sequences. Since we use a unified method, we can compare the contractive conditions very easily. We also discuss the contractive conditions of integral type by a unified method.
TL;DR: In this paper, an extension of the Pareto optimization criterion to locally complete locally convex vector spaces is proposed to guarantee the existence of fixed points of set-valued maps.
Abstract: We prove an extension of the Pareto optimization criterion to locally complete locally convex vector spaces to guarantee the existence of fixed points of set-valued maps.
TL;DR: In this article, an iterative method to approximate solutions of a hierarchical fixed point problem and a variational inequality problem involving a finite family of nonexpansive mappings on a real Hilbert space is introduced and studied.
Abstract: The purpose of this work is to introduce and study an iterative method to approximate solutions of a hierarchical fixed point problem and a variational inequality problem involving a finite family of nonexpansive mappings on a real Hilbert space. Further, we prove that the sequence generated by the proposed iterative method converges to a solution of the hierarchical fixed point problem for a finite family of nonexpansive mappings which is the unique solution of the variational inequality problem. The results presented in this paper are the extension and generalization of some previously known results in this area. An example which satisfies all the conditions of the iterative method and the convergence result is given.