Showing papers in "Fixed Point Theory and Applications in 2012"
TL;DR: In this article, a new concept of contraction was introduced and a fixed point theorem which generalizes Banach contraction principle in a different way than in the known results from the literature was proved.
Abstract: In the article, we introduce a new concept of contraction and prove a fixed point theorem which generalizes Banach contraction principle in a different way than in the known results from the literature. The article includes an example which shows the validity of our results, additionally there is delivered numerical data which illustrates the provided example. MSC: 47H10; 54E50
661 citations
TL;DR: In this article, a fixed point theorem for set-valued quasi-contraction maps in b-metric spaces is given, which extends and generalizes several well known comparable results in the existing literature.
Abstract: In this article, we give a fixed point theorem for set-valued quasi-contraction maps in b-metric spaces. This theorem extends, unifies and generalizes several well known comparable results in the existing literature.
210 citations
TL;DR: In this paper, the fixed point theory in metric-like spaces was initiated and some new fixed point results in partial metric spaces were derived, unifying and generalizing some well-known results in the literature.
Abstract: By a metric-like space, as a generalization of a partial metric space, we mean a pair , where X is a nonempty set and satisfies all of the conditions of a metric except that may be positive for . In this paper, we initiate the fixed point theory in metric-like spaces. As an application, we derive some new fixed point results in partial metric spaces. Our results unify and generalize some well-known results in the literature. MSC:47H10.
197 citations
TL;DR: In this article, Suzuki's fixed point results from (Suzuki, Proc. Am. Math. Soc. 136:1861-1869, 2008) were extended to the case of metric type spaces and cone metric types.
Abstract: Suzuki’s fixed point results from (Suzuki, Proc. Am. Math. Soc. 136:1861-1869, 2008) and (Suzuki, Nonlinear Anal. 71:5313-5317, 2009) are extended to the case of metric type spaces and cone metric type spaces. Examples are given to distinguish our results from the known ones. MSC:47H10, 54H25.
162 citations
TL;DR: In this paper, the notion of -contractive multifunctions was introduced and a fixed-point result for self-maps in complete metric spaces satisfying a contractive condition was obtained.
Abstract: Recently Samet, Vetro and Vetro introduced the notion of α-ψ-contractive type mappings and established some fixed point theorems in complete metric spaces. In this paper, we introduce the notion of -contractive multifunctions and give a fixed point result for these multifunctions. We also obtain a fixed point result for self-maps in complete metric spaces satisfying a contractive condition.
160 citations
TL;DR: In this article, the authors discuss the concept of G-metric spaces and the fixed point existing results of contractive mappings defined on such spaces, and show that the most obtained fixed point theorems on these spaces can be deduced immediately from fixed point Theorem 1.
Abstract: We discuss the introduced concept of G-metric spaces and the fixed point existing results of contractive mappings defined on such spaces. In particular, we show that the most obtained fixed point theorems on such spaces can be deduced immediately from fixed point theorems on metric or quasi-metric spaces. MSC:47H10, 11J83.
129 citations
TL;DR: In this article, an implicit algorithm for two finite families of nonexpansive maps in hyperbolic spaces is proposed and analyzed, and results concerning Δ-convergence and strong convergence are proved.
Abstract: In this article, we propose and analyze an implicit algorithm for two finite families of nonexpansive maps in hyperbolic spaces. Results concerning Δ-convergence as well as strong convergence of the proposed algorithm are proved. Our results are refinement and generalization of several recent results in CAT(0) spaces and uniformly convex Banach spaces. Mathematics Subject Classification (2010): Primary: 47H09; 47H10; Secondary: 49M05.
105 citations
TL;DR: In this paper, the fixed point results for generalized weakly contractive mappings defined on a partial metric space were proved and shown to unify, generalize and complement known comparable results from the current literature.
Abstract: In this article, we prove some fixed point results for generalized weakly contractive mappings defined on a partial metric space. We provide some examples to validate our results. These results unify, generalize and complement various known comparable results from the current literature. AMS Classification 2010: 47H10; 54H25; 54E50.
100 citations
TL;DR: In this article, the concept of coupled best proximity point and cyclic contraction pair is introduced and the existence and convergence of these points in metric spaces is studied. And new results on the existence of coupled fixed points in a uniformly convex Banach space are given.
Abstract: In this article the concept of coupled best proximity point and cyclic contraction pair are introduced and then we study the existence and convergence of these points in metric spaces. We also establish new results on the existence and convergence in a uniformly convex Banach spaces. Furthermore, we give new results of coupled fixed points in metric spaces and give some illustrative examples. An open problems are also given at the end for further investigation.
97 citations
TL;DR: In this paper, the authors studied coupled coincidence and coupled common fixed point theorems in ordered generalized metric spaces for nonlinear contraction condition related to a pair of altering distance functions.
Abstract: In this article, we study coupled coincidence and coupled common fixed point theorems in ordered generalized metric spaces for nonlinear contraction condition related to a pair of altering distance functions. Our results generalize and modify several comparable results in the literature. 2000 MSC: 54H25; 47H10; 54E50.
94 citations
TL;DR: In this article, the authors established some common fixed point theorems for a hybrid pair {g, T} of single valued and multi-valued maps satisfying a generalized contractive condition defined on G-metric spaces.
Abstract: In this article, we establish some common fixed point theorems for a hybrid pair {g, T} of single valued and multi-valued maps satisfying a generalized contractive condition defined on G-metric spaces. Our results unify, generalize and complement various known comparable results from the current literature. 2000 MSC: 54H25; 47H10; 54E50.
TL;DR: In this paper, the fixed point theorems for mappings satisfying cyclical generalized contractive conditions in complete partial metric spaces are given, and fixed point bounds on the number of mappings required to satisfy each condition are given.
Abstract: In this article, we give some fixed point theorems for mappings satisfying cyclical generalized contractive conditions in complete partial metric spaces.
TL;DR: In this article, the authors present triplet coincidence point theorems for F: X3 → X and g: X → X satisfying weak φ-contractions in partially ordered metric spaces.
Abstract: In this article, we present tripled coincidence point theorems for F: X3 → X and g: X → X satisfying weak φ-contractions in partially ordered metric spaces. We also provide nontrivial examples to illustrate our results and new concepts presented herein. Our results unify, generalize and complement various known comparable results from the current literature, Berinde and Borcut and Abbas et al.
TL;DR: In this paper, the results for nonlinear contraction mappings having a mixed monotone property in a partially ordered G-metric space due to Choudhury and Maity are extended and unified.
Abstract: Coupled fixed point results for nonlinear contraction mappings having a mixed monotone property in a partially ordered G-metric space due to Choudhury and Maity are extended and unified. We also provide example to validate the main results in this article. Mathematics Subject classification (2000): 47H10; 54H25.
TL;DR: In this paper, the existence of a unique best proximity point for Geraghty contractions is proved and sufficient conditions for its existence are provided, which is an extension of a result due to Gaghty (Proc. Am. Math. Soc. 40:604-608, 1973).
Abstract: The purpose of this paper is to provide sufficient conditions for the existence of a unique best proximity point for Geraghty-contractions. Our paper provides an extension of a result due to Geraghty (Proc. Am. Math. Soc. 40:604-608, 1973).
TL;DR: In this paper, the authors present some new examples in cone b-metric spaces and prove some fixed point theorems of contractive mappings without the assumption of normality.
Abstract: In this paper we present some new examples in cone b-metric spaces and prove some fixed point theorems of contractive mappings without the assumption of normality in cone b-metric spaces. The results not only directly improve and generalize some fixed point results in metric spaces and b-metric spaces, but also expand and complement some previous results in cone metric spaces. In addition, we use our results to obtain the existence and uniqueness of a solution for an ordinary differential equation with a periodic boundary condition.
TL;DR: In this article, the authors obtain, in the setting of metric spaces or ordered metric spaces, coincidence point and common fixed point theorems for self-mappings in a general class of contractions defined by an implicit relation.
Abstract: In this article we obtain, in the setting of metric spaces or ordered metric spaces, coincidence point, and common fixed point theorems for self-mappings in a general class of contractions defined by an implicit relation. Our results unify, extend, generalize many related common fixed point theorems from the literature. Mathematics Subject Classification (2000): 47H10, 54H25.
TL;DR: In this paper, the authors prove some coincidence and common fixed point results for three mappings satisfying a generalized weak contractive condition in ordered partial metric spaces, and they also give a unique fixed point result for a mapping satisfying a weak cyclical conditional condition.
Abstract: We prove some coincidence and common fixed point results for three mappings satisfying a generalized weak contractive condition in ordered partial metric spaces. As application of the presented results, we give a unique fixed point result for a mapping satisfying a weak cyclical contractive condition. We also provide some illustrative examples. MSC:47H10, 54H25.
TL;DR: In this paper, the authors presented fixed point results for weakly contractive and weakly Kannan mappings in such a way that the classical metric counterpart results are retrieved as a particular case.
Abstract: In this paper, we continue the study of contractive conditions for mappings in complete partial metric spaces. Concretely, we present fixed point results for weakly contractive and weakly Kannan mappings in such a way that the classical metric counterpart results are retrieved as a particular case. Special attention to the cyclical case is paid. Moreover, the well-posedness of the fixed point problem associated to weakly (cyclic) contractive and weakly (cyclic) Kannan mappings is discussed, and it is shown that these contractive mappings are both good Picard operators and special good Picard operators.
TL;DR: In this paper, the existence of a coupled fixed point theorem of nonlinear contraction mappings in complete metric spaces without the mixed monotone property was shown. And the necessary condition for the uniqueness of a coupling fixed point of the given mapping was studied.
Abstract: In this paper, we show the existence of a coupled fixed point theorem of nonlinear contraction mappings in complete metric spaces without the mixed monotone property and give some examples of a nonlinear contraction mapping, which is not applied to the existence of coupled fixed point by using the mixed monotone property. We also study the necessary condition for the uniqueness of a coupled fixed point of the given mapping. Further, we apply our results to the existence of a coupled fixed point of the given mapping in partially ordered metric spaces. Moreover, some applications to integral equations are presented.
TL;DR: In this paper, the authors introduce the notion of almost generalized (ψ, ϕ)-contractive mappings in ordered metric spaces and establish some fixed and common fixed point results in ordered complete metric spaces.
Abstract: In this article, we introduce the notion of almost generalized (ψ, ϕ)-contractive mappings in ordered metric spaces and we establish some fixed and common fixed point results in ordered complete metric spaces. Our results generalize several well-known comparable results in the literature. Finally, an example and an application are given in order to support the useability of our results.
TL;DR: In this paper, a mixed g-monotone mapping F : X3 → X satisfying (ψ, ϕ)-contractions in ordered generalized metric spaces is studied.
Abstract: In this paper, we establish some tripled coincidence point results for a mixed g-monotone mapping F : X3 → X satisfying (ψ, ϕ)-contractions in ordered generalized metric spaces. Also, an application and some examples are given to support our results.
TL;DR: In this paper, Sintunavarat and Kumam proved fixed point theorems for mappings satisfying certain point-dependent contractive conditions, which were later confirmed by Rouzkard and Imdad.
Abstract: Owning the concept of complex valued metric spaces introduced by Azam et al., we prove several fixed point theorems for mappings satisfying certain point-dependent contractive conditions. The main results announced by Sintunavarat and Kumam (J. Inequal. Appl. 2012:84, 2012), Rouzkard and Imdad (Comput. Math. Appl., 2012, doi:10.1016/j.camwa.2012.02.063), and Dass and Gupta (Indian J. Pure Appl. Math. 6(12):1455-1458, 1975) are deduced from our results under weaker assumptions.
TL;DR: In this paper, the authors present best proximity point theorems for new classes of non-self mappings, known as generalized proximal contractions, in the setting of metric spaces.
Abstract: Best proximity point theorems unravel the techniques for determining an optimal approximate solution, designated as a best proximity point, to the equation Tx = x which is likely to have no solution when T is a non-self mapping. This article presents best proximity point theorems for new classes of non-self mappings, known as generalized proximal contractions, in the setting of metric spaces. Further, the famous Banach's contraction principle and some of its generalizations and variants are realizable as special cases of the aforesaid best proximity point theorems.
TL;DR: In this article, the existence and uniqueness of fixed points of a general class of contractive mappings on complete rectangular metric spaces are discussed and a generalization of a fixed point theorem recently introduced by Lakzian and Samet is introduced.
Abstract: Existence and uniqueness of fixed points of a general class of contractive mappings on complete rectangular metric spaces are discussed. One of the theorems is a generalization of a fixed point theorem recently introduced by Lakzian and Samet. Fixed points of contractions under conditions involving rational expressions are also investigated. Several particular cases and applications as well as an illustrative example are given. MSC:46T99, 47H10, 54H25.
TL;DR: In this paper, a general common fixed point theorem for two pairs of weakly compatible self-mappings of a partial metric space satisfying a generalized Meir-Keeler type contractive condition was proved.
Abstract: In this article, we prove a general common fixed point theorem for two pairs of weakly compatible self-mappings of a partial metric space satisfying a generalized Meir-Keeler type contractive condition The presented theorem extends several well known results in literature
TL;DR: In this paper, the authors extend the results of Harjani and Sadarangani and some other authors and prove a new fixed point theorem of a contraction mapping in a complete metric space endowed with a partial order by using altering distance functions.
Abstract: The aim of this paper is to extend the results of Harjani and Sadarangani and some other authors and to prove a new fixed point theorem of a contraction mapping in a complete metric space endowed with a partial order by using altering distance functions. Our theorem can be used to investigate a large class of nonlinear problems. As an application, we discuss the existence of a solution for a periodic boundary value problem.
TL;DR: In this article, the concepts of W-compatible mappings for mappings F : X × D × X × X → X and g : X → D → X,w here (X, d) is an abstract metric space.
Abstract: In this paper, we introduce the concepts of W-compatible mappings for mappings F : X × X × X → X and g : X → X ,w here (X, d) is an abstract metric space. We establish tripled coincidence and common tripled fixed point theorems in such spaces. The presented theorems generalize and extend several well-known comparable results in literature, in particular the results of Abbas, Ali and Radenovi´ (Appl. Math. Comput. 217:195-202, 2010). We also provide an example to illustrate our obtained results. MSC: 54H25; 47H10
TL;DR: In this paper, a coupled fixed point theorem for nonlinear contractive mappings in the framework of a metric space endowed with partial order is proved and the uniqueness of such mappings is proved.
Abstract: The object of this paper is to determine some coupled fixed point theorems for nonlinear contractive mappings in the framework of a metric space endowed with partial order. We also prove the uniqueness of a coupled fixed point for such mappings in this setup.
TL;DR: In this paper, the authors proved quadruple coincidence and common fixed point theorems for generalized contractions in partially ordered metric spaces, which unify, generalize and complement various known results from the current literature.
Abstract: In this manuscript, we prove some quadruple coincidence and common fixed point theorems for F : X 4 ® X and g : X ® X satisfying generalized contractions in partially ordered metric spaces. Our results unify, generalize and complement various known results from the current literature. Also, an application to matrix equations is given. 2000 Mathematics subject Classifications: 46T99; 54H25; 47H10; 54E50.