Showing papers in "Fixed Point Theory and Applications in 2010"
TL;DR: In this article, the authors extend the celebrated result of W. A. Kirk that a metric space is complete if and only if every Caristi self-mapping for has a fixed point, to partial metric spaces.
Abstract: We extend the celebrated result of W. A. Kirk that a metric space is complete if and only if every Caristi self-mapping for has a fixed point, to partial metric spaces.
243 citations
TL;DR: In this paper, the authors present some fixed point results for nondecreasing and weakly increasing operators in a partially ordered metric space using implicit relations, and give an existence theorem for common solution of two integral equations.
Abstract: We present some fixed point results for nondecreasing and weakly increasing operators in a partially ordered metric space using implicit relations. Also we give an existence theorem for common solution of two integral equations.
241 citations
TL;DR: In this paper, the authors prove some fixed point results for self-mapping in a complete -metric space under some contractive conditions related to a nondecreasing map with for all.
Abstract: We prove some fixed point results for self-mapping in a complete -metric space under some contractive conditions related to a nondecreasing map with for all . Also, we prove the uniqueness of such fixed point, as well as studying the -continuity of such fixed point.
182 citations
TL;DR: Several fixed point and common fixed point theorems are obtained in the setting of metric-type spaces introduced by M. A. Khamsi in 2010 as discussed by the authors, which is a special case of fixed point spaces.
Abstract: Several fixed point and common fixed point theorems are obtained in the setting of metric-type spaces introduced by M. A. Khamsi in 2010.
163 citations
TL;DR: In this article, the newly introduced concept of cone metric spaces is discussed and the fixed point existence results of contractive mappings defined on such metric spaces are shown to be merely copies of the classical ones.
Abstract: We discuss the newly introduced concept of cone metric spaces. We also discuss the fixed point existence results of contractive mappings defined on such metric spaces. In particular, we show that most of the new results are merely copies of the classical ones.
145 citations
TL;DR: In this paper, a strong convergence theorem of an iterative sequence in CAT(0) spaces was proved for a family of non-self mappings, and the authors applied their result to find a common fixed point of a class of nonexpansive mappings.
Abstract: Motivated by Halpern's result, we prove strong convergence theorem of an iterative sequence in CAT(0) spaces. We apply our result to find a common fixed point of a family of nonexpansive mappings. A convergence theorem for nonself mappings is also discussed.
101 citations
TL;DR: In this article, the authors prove the demiclosed principle for asymptotically nonexpansive mappings in CAT(0) spaces, and obtain a -convergence theorem of the Krasnosel'skii-Mann iteration for this setting.
Abstract: We prove the demiclosed principle for asymptotically nonexpansive mappings in CAT(0) spaces. As a consequence, we obtain a -convergence theorem of the Krasnosel'skii-Mann iteration for asymptotically nonexpansive mappings in this setting. Our results extend and improve many results in the literature.
75 citations
TL;DR: In this paper, a modified hybrid projection algorithm is proposed to approximate a common fixed point of a -strict pseudocontraction and of two sequences of nonexpansive mappings.
Abstract: We propose a modified hybrid projection algorithm to approximate a common fixed point of a -strict pseudocontraction and of two sequences of nonexpansive mappings. We prove a strong convergence theorem of the proposed method and we obtain, as a particular case, approximation of solutions of systems of two equilibrium problems.
72 citations
TL;DR: In this paper, the authors studied an initial value problem for a coupled Caputo type nonlinear fractional differential system of higher order, where the nonhomogeneous terms in the fractional derivatives of lower orders are allowed to depend on the unknown functions together with a fractional derivative of lower order.
Abstract: We study an initial value problem for a coupled Caputo type nonlinear fractional differential system of higher order. As a first problem, the nonhomogeneous terms in the coupled fractional differential system depend on the fractional derivatives of lower orders only. Then the nonhomogeneous terms in the fractional differential system are allowed to depend on the unknown functions together with the fractional derivative of lower orders. Our method of analysis is based on the reduction of the given system to an equivalent system of integral equations. Applying the nonlinear alternative of Leray-Schauder, we prove the existence of solutions of the fractional differential system. The uniqueness of solutions of the fractional differential system is established by using the Banach contraction principle. An illustrative example is also presented.
58 citations
TL;DR: In this paper, Mihail and Miculescu introduced the notion of GIFS, which is a family of functions where is a complete metric space (in the case when is a compact metric space was studied) and.
Abstract: The aim of this paper is to continue the research work that we have done in a previous paper published in this journal (see Mihail and Miculescu, 2008). We introduce the notion of GIFS, which is a family of functions , where is a complete metric space (in the above mentioned paper the case when is a compact metric space was studied) and . In case that the functions are Lipschitz contractions, we prove the existence of the attractor of such a GIFS and explore its properties (among them we give an upper bound for the Hausdorff-Pompeiu distance between the attractors of two such GIFSs, an upper bound for the Hausdorff-Pompeiu distance between the attractor of such a GIFS, and an arbitrary compact set of and we prove its continuous dependence in the 's). Finally we present some examples of attractors of GIFSs. The last example shows that the notion of GIFS is a natural generalization of the notion of IFS.
56 citations
TL;DR: In this article, some mutual relations between p-cyclic contractive self-mappings and Meir-Keeler P-Cyclic Contractive Self-Mappings are discussed, and related results about the best proximity points and existence and uniqueness of fixed points are also formulated.
Abstract: Some mutual relations between p-cyclic contractive self-mappings, p-cyclic Kannan self-mappings, and Meir-Keeler p-cyclic contractions are stated. On the other hand, related results about the existence of the best proximity points and existence and uniqueness of fixed points are also formulated.
TL;DR: In this paper, the fixed point and coincidence results for multivalued generalized weak contractive mappings on complete metric spaces were presented. But the results were not extended to the case of generalized weak contracts.
Abstract: Fixed point and coincidence results are presented for multivalued generalized -weak contractive mappings on complete metric spaces, where is a lower semicontinuous function with and for all Our results extend previous results by Zhang and Song (2009), as well as by Rhoades (2001), Nadler (1969), and Daffer and Kaneko (1995)
TL;DR: In this paper, the authors prove two general fixed theorems for maps in -metric spaces and then show that these maps satisfy property properties. But they do not consider the case of maps in 2D spaces.
Abstract: We prove two general fixed theorems for maps in -metric spaces and then show that these maps satisfy property .
TL;DR: In this article, the main aim is to study and establish coupled fixed point theorems for nonlinear contractive maps that satisfied Mizoguchi-Takahashi's condition in the setting of quasiordered metric spaces or usual metric spaces.
Abstract: The main aim of this paper is to study and establish some new coupled fixed point theorems for nonlinear contractive maps that satisfied Mizoguchi-Takahashi's condition in the setting of quasiordered metric spaces or usual metric spaces.
TL;DR: In this paper, the existence of common fixed points for a commuting pair consisting of a single-valued and a multivalued mapping both satisfying the Suzuki condition in a uniformly convex Banach space was proved.
Abstract: In the first part of this paper, we prove the existence of common fixed points for a commuting pair consisting of a single-valued and a multivalued mapping both satisfying the Suzuki condition in a uniformly convex Banach space. In this way, we generalize the result of Dhompongsa et al. (2006). In the second part of this paper, we prove a fixed point theorem for upper semicontinuous mappings satisfying the Suzuki condition in strictly spaces; our result generalizes a recent result of Dominguez-Benavides et al. (2009).
TL;DR: In this paper, the theory of topological vector space valued cone metric spaces with non-normal cones was developed and three general fixed point results in these spaces were proved and deduce as corollaries several extensions of theorems about fixed points and common fixed points.
Abstract: We develop the theory of topological vector space valued cone metric spaces with nonnormal cones. We prove three general fixed point results in these spaces and deduce as corollaries several extensions of theorems about fixed points and common fixed points, known from the theory of (normed-valued) cone metric spaces. Examples are given to distinguish our results from the known ones.
TL;DR: In this paper, Berinde et al. present some (local and global) fixed point results for singlevalued and multivalued generalized contractions on spaces endowed with vector-valued metrics.
Abstract: The purpose of this work is to present some (local and global) fixed point results for singlevalued and multivalued generalized contractions on spaces endowed with vector-valued metrics. The results are extensions of some theorems given by Perov (1964), Bucur et al. (2009), M. Berinde and V. Berinde (2007), O'Regan et al. (2007), and so forth.
TL;DR: In this article, the authors present a fixed point theorem for generalized contractions in partially ordered complete metric spaces. And they also present an application to first-order ordinary differential equations, which is a generalization of the generalized contraction theorem presented in this paper.
Abstract: The purpose of this paper is to present a fixed point theorem for generalized contractions in partially ordered complete metric spaces. We also present an application to first-order ordinary differential equations.
TL;DR: Two different kinds of fixed point theorems on ordered nonArchimedean fuzzy metric spaces are provided and a common fixed point theorem is given for noncontractive type mappings.
Abstract: In the present paper we provide two different kinds of fixed point theorems on ordered nonArchimedean fuzzy metric spaces. First, two fixed point theorems are proved for fuzzy order -contractive type mappings. Then a common fixed point theorem is given for noncontractive type mappings. Kirk's problem on an extension of Caristi's theorem is also discussed.
TL;DR: In this article, a positive answer to a question raised by Al-Thagafi and Shahzad (Nonlinear Analysis, 70 (2009), 3665-3671) about best proximity points of cyclic contractions on reflexive Banach spaces was provided.
Abstract: We provide a positive answer to a question raised by Al-Thagafi and Shahzad (Nonlinear Analysis, 70 (2009), 3665-3671) about best proximity points of cyclic -contractions on reflexive Banach spaces.
TL;DR: In this article, a partial quasiordering in cone uniform spaces with generalized pseudodistances for giving the general maximality principle in these spaces is introduced, which can be used to obtain new and general results of Ekeland and Caristi types without lower semicontinuity assumptions.
Abstract: Our aim is twofold: first, we want to introduce a partial quasiordering in cone uniform spaces with generalized pseudodistances for giving the general maximality principle in these spaces. Second, we want to show how this maximality principle can be used to obtain new and general results of Ekeland and Caristi types without lower semicontinuity assumptions, which was not done in the previous publications on this subject.
TL;DR: In this article, a nonempty closed convex subset of a complete CAT(0) space with the nearest point projection from onto a non-self mapping with iteratively by,,, where and are real sequences in for some then -converges to some point in
Abstract: Suppose that is a nonempty closed convex subset of a complete CAT(0) space with the nearest point projection from onto Let be a nonexpansive nonself mapping with Suppose that is generated iteratively by , , , where and are real sequences in for some Then -converges to some point in This is an analog of a result in Banach spaces of Shahzad (2005) and extends a result of Dhompongsa and Panyanak (2008) to the case of nonself mappings
TL;DR: In this article, the authors studied the existence of fixed points and convergence of iterates for asymptotic pointwise contractions in uniformly convex metric spaces and showed that fixed points are necessary and sufficient for set-valued mappings in the same class of spaces.
Abstract: We study the existence of fixed points and convergence of iterates for asymptotic pointwise contractions in uniformly convex metric spaces. We also study the existence of fixed points for set-valued nonexpansive mappings in the same class of spaces. Our results do not assume convexity of the metric which makes a big difference when studying the existence of fixed points for set-valued mappings.
TL;DR: In this article, the convergence of Ishikawa iterative processes for the class of asymptotically pseudocontractive mappings in the intermediate sense is studied and weak convergence theorems are established.
Abstract: A new nonlinear mapping is introduced. The convergence of Ishikawa iterative processes for the class of asymptotically pseudocontractive mappings in the intermediate sense is studied. Weak convergence theorems are established. A strong convergence theorem is also established without any compact assumption by considering the so-called hybrid projection methods.
TL;DR: In this paper, the existence of a common solution for certain class of functional equations arising in dynamic programming, under much weaker conditions, is discussed. And the results obtained here in generalize many well known results.
Abstract: Coincidence and fixed point theorems for a new class of hybrid contractions consisting of a pair of single-valued and multivalued maps on an arbitrary nonempty set with values in a metric space are proved. In addition, the existence of a common solution for certain class of functional equations arising in dynamic programming, under much weaker conditions are discussed. The results obtained here in generalize many well known results.
TL;DR: In this paper, the existence of approximate fixed points and approximate endpoints for multivalued almost-contractions is established and quantitative estimates of the sets of approximations are developed.
Abstract: The existence of approximate fixed points and approximate endpoints of the multivalued almost -contractions is established. We also develop quantitative estimates of the sets of approximate fixed points and approximate endpoints for multivalued almost -contractions. The proved results unify and improve recent results of Amini-Harandi (2010), M. Berinde and V. Berinde (2007), Ciric (2009), M. Pacurar and R. V. Pacurar (2007) and many others.
TL;DR: In this paper, the authors obtained common fixed points of a pair of mappings satisfying a generalized contractive type condition in TVS-valued cone metric spaces, which generalize some well-known recent results in the literature.
Abstract: We obtain common fixed points of a pair of mappings satisfying a generalized contractive type condition in TVS-valued cone metric spaces. Our results generalize some well-known recent results in the literature.
TL;DR: In this paper, the authors introduce partially ordered -fuzzy metric spaces and prove a common fixed point theorem in these spaces, and prove the same result for fixed points in the Euclidean metric space.
Abstract: We introduce partially ordered -fuzzy metric spaces and prove a common fixed point theorem in these spaces.
TL;DR: In this paper, the sum of a weakly-strongly continuous map and a nonexpansive map on a Banach space is shown to be a fixed point theorem.
Abstract: We present some fixed point theorems for the sum of a weakly-strongly continuous map and a nonexpansive map on a Banach space . Our results cover several earlier works by Edmunds, Reinermann, Singh, and others.
TL;DR: In this article, the successive approximation method for proving the Hyers-Ulam stability of a nonlinear integral equation was applied to prove the stability of an integral equation with respect to a nonparametric integral equation.
Abstract: We will apply the successive approximation method for proving the Hyers-Ulam stability of a nonlinear integral equation.