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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.

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.

The paper concerns our sustained efforts for introduction of V-fuzzy metric spaces and to study their basic topological properties. As an application of this concept, we prove coupled common fixed point theorems for mixed weakly monotone maps in partially ordered V-fuzzy metric spaces. An example quoted in this paper also corroborates fully the main result. Also, here we introduce the concept of a symmetric V-fuzzy metric space. Under the influence of symmetry property of V-fuzzy metric spaces, its conversion materializes to the main result from V-fuzzy metric spaces to fuzzy metric spaces.

The aim of this paper to present fixed point results for single-valued operators in b-metric spaces. The case of scalar metric and the case of vector-valued metric approaches are considered. As an application, a system of integral equations is studied.

A lot of authors have proved various common fixed-point results for pairs of self-mappings under strict contractive conditions in metric spaces. In the case of cone metric spaces, fixed point results are usually proved under assumption that the cone is normal. In the present paper we prove common fixed point results under strict contractive conditions in cone metric spaces using only the assumption that the cone interior is nonempty. We modify the definition of property (E.A), introduced recently in the work by Aamri and Moutawakil (2002), and use it instead of usual assumptions about commutativity or compatibility of the given pair. Examples show that the obtained results are proper extensions of the existing ones.

The notion of modular metric space, being a natural generalization of classical modulars over linear spaces, was recently introduced. In this paper, we introduce a generalized F-contraction in modular metric space and investigate the existence of fixed points for such contractions. As applications, we derive some new fixed point theorems in partially ordered modular metric spaces, Suzuki type fixed point theorems in modular metric spaces and fixed point theorems for contractions involving integral inequalities. Moreover, we deduce new fixed point results in triangular fuzzy metric spaces and provide some examples to illustrate the usability of the obtained results.

In this paper, we obtain sufficient conditions for the existence of fixed points for monotone quasi-contraction mappings in metric and modular metric spaces endowed with a graph. This is the extension of Ran and Reurings and Jachymski fixed point theorems for monotone contraction mappings in partially ordered metric spaces and in metric spaces endowed with a graph to the case of quasi-contraction mappings introduced by Ciric.

In this paper, owing to the concept of F-contraction, we define two new classes of functions M(S, T )a ndN(S, T), and we prove some new fixed point results for single-valued and multivalued mappings in complete metric spaces. Our results extend, generalize and unify several known results in the literature. We include an example to show that the generalization is proper. MSC: Primary 30C45; 30C10; secondary 47B38

The purpose of this paper is to introduce some basic definitions about fixed point and best proximity point in two classes of probabilistic metric spaces and to prove contraction mapping principle and relevant best proximity point theorems. The first class is the so-called S-probabilistic metric spaces. In S-probabilistic metric spaces, the generalized contraction mapping principle and generalized best proximity point theorems have been proved by authors. These results improve and extend the recent results of Su and Zhang (Fixed Point Theory Appl. 2014:170, 2014). The second class is the so-called Menger probabilistic metric spaces. In Menger probabilistic metric spaces, the contraction mapping principle and relevant best proximity point theorems have been proved by authors. These results also improve and extend the results of many authors. In order to get the results of this paper, some new methods have been used. Meanwhile some error estimate inequalities have been established.

Sedghi et al. (Mat. Vesn. 64(3):258-266, 2012) introduced the notion of a S-metric as a generalized metric in 3-tuples S : X 3 → [ 0 , ∞ ) $S:X^{3} \rightarrow[0,\infty)$ , where X is a nonempty set. The aim of this paper is to introduce the concept of an n-tuple metric A : X n → [ 0 , ∞ ) $A: X^{n} \rightarrow[0,\infty)$ and to study its basic topological properties. We also prove some generalized coupled common fixed point theorems for mixed weakly monotone maps in partially ordered A-metric spaces. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature.

We introduce a new concept of generalized metric spaces for which we extend some well-known fixed point results including Banach contraction principle, Ciric’s fixed point theorem, a fixed point result due to Ran and Reurings, and a fixed point result due to Nieto and Rodriguez-Lopez. This new concept of generalized metric spaces recover various topological spaces including standard metric spaces, b-metric spaces, dislocated metric spaces, and modular spaces.

We discuss multivalued weakly Picard operators on partial Hausdorff metric spaces. First, we obtain Kikkawa-Suzuki type fixed point theorems for a new type of generalized contractive conditions. Then, we prove data dependence of a fixed points set theorem. Finally, we present sufficient conditions for well-posedness of a fixed point problem. Our results generalize, complement and extend classical theorems in metric and partial metric spaces.

We give a generalization of the Banach contraction principle on a modular metric space endowed with a graph. The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces, were recently introduced. This paper can be seen as the modular metric version of Jachymski’s fixed point result for mappings on a metric space with a graph.

In this paper, by using Minkowski functional introduced by Kadelburg et al. (Appl. Math. Lett. 24:370-374, 2011) or nonlinear scalarization function introduced by Du (Nonlinear Anal. 72:2259-2261, 2010), we prove some equivalences between vectorial versions of fixed point theorems for H-cone metrics in the sense of Arshad and Ahmad and scalar versions of fixed point theorems for (general) Hausdorff-Pompeiu metrics (in usual sense).

We consider quasicontraction nonself-mappings on Takahashi convex metric spaces and common fixed point theorems for a pair of maps. Results generalizing and unifying fixed point theorems of Ivanov, Jungck, Das and Naik, and Ćirić are established.

In this paper we prove a coincidence point result in a space which does not have to satisfy any of the classical axioms that define a metric space. Furthermore, the ambient space need not be ordered and does not have to be complete. Then, this result may be applied in a wide range of different settings (metric spaces, quasi-metric spaces, pseudo-metric spaces, semi-metric spaces, pseudo-quasi-metric spaces, partial metric spaces, G-spaces, etc.). Finally, we illustrate how this result clarifies and improves some well-known, recent results on this topic.

In this note, we establish the equivalence between recent fixed point theorems involving quasicontractive type mappings in metric spaces endowed with a partial order. MSC:47H10.

In this paper, we introduce the notion of a quasi-contraction restricted with a linear bounded mapping in cone metric spaces, and prove a unique fixed point theorem for this quasi-contraction without the normality of the cone. It is worth mentioning that the main result in this paper could not be derived from ´ Ciri´ c’s result by the scalarization method, and hence indeed improves many recent results in cone metric spaces. MSC: 06A07; 47H10

Recently, Khamsi and Hussain (Nonlinear Anal. 73:3123-3129, 2010) discussed a natural topology defined on any metric type space and noted that this topology enjoys most of the metric topology like properties. In this paper, we define topologically complete type metrizable space and prove that being of metrizability type is preserved under a countable Cartesian product and establish the fact that any G δ set in a complete metric type space is a topologically metrizable type space. Next, we introduce the concept of wt-distance on a metric type space and prove some fixed point theorems in a partially ordered metric type space with some weak contractions induced by the wt-distance. MSC:47H09, 47H10.

In this paper, we obtain some common fixed point results for the mappings satisfying rational expressions on a closed ball in complex valued metric spaces. Our results improve several well-known conventional results. MSC:47H10, 54H25.

In 1994, Matthews introduced and studied the concept of partial metric space and obtained a Banach-type fixed point theorem on complete partial metric spaces. In this paper we study fixed point results of new mappings with a contractive iterate at a point in partial metric spaces. Our results generalize and unify some results of Sehgal, Guseman and Ćirić for mappings with a generalized contractive iterate at a point to partial metric spaces. We give some generalized versions of the fixed point theorem of Matthews. The theory is illustrated by some examples.

Very recently, Isik and Turkoglu (Fixed Point Theory Appl. 2013:131, 2013) proved a common fixed point theorem in a rectangular metric space by using three auxiliary distance functions. In this paper, we note that this result can be derived from the recent paper of Lakzian and Samet (Appl. Math. Lett. 25:902-906, 2012). MSC:47H10, 54H25.

In this paper, by using -type real functions, some fixed point theorems for complex non-self mappings satisfying an implicit relation in two fuzzy metric spaces in the sense of Kaleva and Seikkala are established. As applications, we obtain the corresponding fixed point theorems for complex non-self mappings satisfying an implicit relation in two Menger probabilistic metric spaces. Also, an example, which shows the validity of the hypotheses of our main results, is given. MSC:47H10, 46S40, 54E70.

In this work, we establish some fixed point theorems for weakly C-contractive mappings in partial metric spaces. Presented theorems extend and generalize some existence results in the literature. Also, an example is given to support our results.

It is shown that if a mapping is a local radial contraction defined on a metric space which takes values in a metric transform of , then for many metric transforms it is also a local radial contraction (with possibly different contraction constant) relative to the original metric. Several specific examples are given. This in turn implies that the mapping has a fixed point if the space is rectifiably pathwise connected. Some results about set-valued contractions are also discussed.

Coincidence point theorems for hybrid pairs of single-valued and multi-valued mappings on an arbitrary non-empty set with values in a partial metric space using a partial Hausdorff metric have been proved. As an application of our main result, the existence and uniqueness of common and bounded solutions of functional equations arising in dynamic programming are discussed.

In this paper, we initiate a study of fixed point results in the setup of partial metric spaces endowed with a graph. The concept of a power graphic contraction pair of two mappings is introduced. Common fixed point results for such maps without appealing to any form of commutativity conditions defined on a partial metric space endowed with a directed graph are obtained. These results unify, generalize and complement various known comparable results from the current literature.

A new metric in the space clos(X) of all closed subsets of a metric space X is proposed. This metric, unlike the generalized Hausdorff metric, takes finite values only, and the convergence of a sequence of closed sets H i , i =1 , 2, ... , with respect to this metric is equivalent to the convergence (in the sense of Hausdorff ) for any r ≥ 0 of the unions of H i with a closed ‘exterior ball’ of radius r. Using this metric allows one to investigate multi-valued maps that have images in clos(X) and are not continuous in the Hausdorff metric. In the work, the necessary and sufficient conditions for a multi-valued map to be continuous and Lipschitz with respect to the metric presented are studied, a connection of these properties with their analogues in the Hausdorff metric is derived, and a generalization of the Nadler fixed point theorem is obtained. MSC: 47H04; 47H10; 54E35

Let (X, � ) be a partially ordered set and d be a complete metric on X. The notion of f -contractive for a set-valued mapping due to Latif and Beg is extended through an implicit relation. Coincidence and fixed point results are obtained for mappings satisfying generalized contractions in a partially ordered metric space X. Our results improve and extend several known results in the existing literature. MSC: 47H10; 47H04; 47H07

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.

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.

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.

The aim of this article is to generalize a result which is obtained by Mizoguchi and Takahashi [J. Math. Anal. Appl. 141, 177-188 (1989)] to the case of cone metric spaces.

The purpose of this paper is to prove some existence theorems for fixed point problem by using a generalization of metric distance, namely u-distance. Consequently, some special cases are discussed and an interesting example is also provided. Presented results are generalizations of the important results due to Ume (Fixed Point Theory Appl 2010(397150), 21 pp, 2010) and Suzuki and Takahashi (Topol Methods Nonlinear Anal 8, 371-382, 1996). 2010 Mathematics Subject Classification: 47H09, 47H10.

In this paper, using the setting of a generalized metric space, a unique common fixed point of four R-weakly commuting maps satisfying a generalized contractive condition is obtained. We also present example in support of our result. 2000 MSC: 54H25; 47H10; 54E50.

Fixed point and common fixed point results for mappings in tvs-cone metric spaces (with the underlying cone which is not normal) under contractive conditions expressed in the terms of c-distance are obtained. Respective results concerning mappings without periodic points are also deduced. Examples are given to distinguish these results from the known ones. Mathematics Subject Classification (2010) 47H10, 54H25

In this article, lower semi-continuous maps are used to generalize Cristi-Kirk's fixed point theorem on partial metric spaces. First, we prove such a type of fixed point theorem in compact partial metric spaces, and then generalize to complete partial metric spaces. Some more general results are also obtained in partial metric spaces. 2000 Mathematics Subject Classification 47H10,54H25

In this paper we consider the so called a cone metric type space, which is a generalization of a cone metric space. We prove some common fixed point theorems for four mappings in those spaces. Obtained results extend and generalize well-known comparable results in the literature. All results are proved in the settings of a solid cone, without the assumption of continuity of mappings.

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.

We prove a result on points of coincidence and common fixed points for three self-mappings satisfying generalized contractive type conditions in cone metric spaces. We deduce some results on common fixed points for two self-mappings satisfying contractive type conditions in cone metric spaces. These results generalize some well-known recent results.

We establish a common fixed point theorem for weakly compatible mappings generalizing a result of Khan and Kubiaczyk (1988). Also, an example is given to support our generalization. We also prove common fixed point theorems for weakly compatible mappings in metric and compact metric spaces.

We first give some fixed point results for set-valued self-map contractions in complete metric spaces. Then we derive a fixed point theorem for nonself set-valued contractions which are metrically inward. Our results generalize many well-known results in the literature.

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.

Cone-valued lower semicontinuous maps are used to generalize Cristi-Kirik's fixed point theorem to Cone metric spaces. The cone under consideration is assumed to be strongly minihedral and normal. First we prove such a type of fixed point theorem in compact cone metric spaces and then generalize to complete cone metric spaces. Some more general results are also obtained in quasicone metric spaces. Copyright (C) 2009 T. Abdeljawad and E. Karapinar.

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.

We define a weaker Meir-Keeler type function and establish the fixed point theorems for a weaker Meir-Keeler type -set contraction in metric spaces.

We establish existence and uniqueness of fixed points for a new class of mappings, by using R-functions and lower semi-continuous functions in the setting of metric spaces. As consequences of this results, we obtain several known fixed point results, in metric and partial metric spaces. An example is given to support the new theory. A homotopy result for operators on a set endowed with a metric is given as application.

In this short note, we announce that all the presented fixed point results in the setting of multiplicative metric spaces can be derived from the corresponding existing results in the context of standard metric spaces in the literature.

After the appearance of Nieto and Rodriguez-Lopez’s theorem, the branch of fixed point theory devoted to the setting of partially ordered metric spaces have attracted much attention in the last years, especially when coupled, tripled, quadrupled and, in general, multidimensional fixed points are studied. Almost all papers in this direction have been forced to present two results assuming two different hypotheses: the involved mapping should be continuous or the metric framework should be regular. Both conditions seem to be different in nature because one of them refers to the mapping and the other one is assumed on the ambient space. In this paper, we unify such different conditions in a unique one. By introducing the notion of continuity of a mapping from a metric space into itself depending on a function α, which is the case that covers the partially ordered setting, we extend some very recent theorems involving control functions that only must be lower/upper semi-continuous from the right. Finally, we use metric spaces endowed with transitive binary relations rather than partial orders.

In this paper, some multifunctions on partial metric space are defined and common fixed points of such multifunctions are discussed. The results presented in the paper generalize some of the existing results in the literature. Several conclusions of the main results are given.