On graphical fuzzy metric spaces and related fixed point theorems

A new related fixed point theorem on two complete metric spaces is obtained. A generalization is given for two compact metric spaces.

In this paper, using the method of Hicks, we prove some new related fixed point theorems for pair of mappings on two d-complete topological spaces under the suitable conditions. We also derive some related fixed point theorems from our main results. Finally, by using w-continuity, we establish a related fixed point theorem in d-complete Hausdorff topological spaces.

Related fixed point theorems on two or three metric spaces have been proved in different ways.However, so for the related fixed point theorem on fuzzy metric spaces have not been proved.Sharma, Deshpande and Thakur were the first who have established related fixed point theorem for four mappings on two complete fuzzy metric spaces.Their work was maiden in this line.In this paper we obtain a related fixed point theorem for six mappings on three complete fuzzy metric spaces.Of course this is a new result on this line.

In a recent paper Xie et al. (Fixed Point Theory Appl. 2013:192, 2013) gave several extensions and some applications of the Abian-Brown (AB) fixed point theorem. While the AB fixed point theorem and its extensions (as well as other related fixed point theorems) assume that the mapping is isotone, this note shows that for single-valued finite maps this condition relates to the acyclicity of the map, which in turn relates to Abian’s (Nieuw Arch. Wiskd. XVI:184-185, 1968) most basic fixed point theorem for finite sets.

In this article, we introduce two new types of generalized contraction mappings in double controlled metric type spaces: Θ-double controlled contraction mapping and Ćirić-Reich-Rus-type-Θ-double controlled contraction mapping. For each contraction mapping, we establish the existence and uniqueness of the fixed point theorems on the complete double controlled metric type space and provide examples. We present an application of our results and demonstrate how our results generalize several existing fixed point theorems in the literature.

<abstract><p>In this paper, we present some fixed point theorems for generalized nonlinear contractions involving a new pair of auxiliary functions in a metric space endowed with a locally finitely $ T $-transitive binary relation. Our newly proved results generalize some well-known fixed point theorems existing in the literature. We also provide an example which substantiates the utility of our results.</p></abstract>

Using the notion of fuzzy negation functions which naturally arises in the theory and applications of fuzzy logic, we enlarge the class of fuzzy ψ-contractions of ( ϵ , λ ) type as well as the class of fuzzy k − ♢ contractions and generalize corresponding fixed point theorems. We show that strict negations, strong negations and Archimedean t-norms play a central role in the aforesaid fixed point theorems. Appropriate examples that illustrate the exposed theory are provided. In the process, we obtain a new type of topology (as well as convergence and completeness) for the fuzzy metric spaces that suggesting a potential new research avenue to explore the subject.

Very recently, Samet et al. and Jleli and Samet reported that most of fixed point results in the context of G-metric space, defined by Sims and Zead, can be derived from the usual fixed point theorems on the usual metric space. In this paper, we state and prove some fixed point theorems in the framework of G-metric space that cannot be obtained from the existence results in the context of associated metric space.

Generalized [formula omitted]-conditions and related fixed point theorems

In this paper we generalize some results of fixed point theory to partial metric spaces by using metric methods in the context of a new extension of Ekeland?s variational principle. We provide some corollaries to unify our results with other existing results in the literature along the same vein. Then, we show that our results require existence assumptions weaker than those for some well-known contractive maps, including the ones in the sense of Banach, Ciric, Song, Kannan and Hardy Rogers. Also, we provide some estimates for the distance to the fixed point set in partial metric space. In order to illustrate the strength of our fixed point theorem, we use it in order to derive a new result on coupled fixed points.

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

The aim of this paper is to introduce two classes of generalized α-ψ-contractive type mappings of integral type and to analyze the existence of fixed points for these mappings in complete metric spaces. Our results are improved versions of a multitude of relevant fixed point theorems of the existing literature. MSC:54H25, 47H10, 54E50.

In this paper, we introduce a new notion to generalize a Mizoguchi-Takahashi type contraction. Then, using this notion, we obtain a fixed point theorem for multivalued maps. Our results generalize some results by Minak and Altun, Kamran and those contained therein. MSC:47H10, 54H25.

In this report, we present some new fixed points theorems in the context of quasi-metric spaces that can be particularized in a wide range of different frameworks (metric spaces, partially ordered metric spaces, G-metric spaces, etc.). Our contractivity conditions involve different classes of functions and we study the case in which they only depend on a unique variable. Furthermore, we do not only introduce new contractivity conditions, but also expansivity conditions. As a consequence of our results, we announce that many fixed point results in G-metric spaces can be derived from the existing results if all arguments are not distinct.

In several ways, related fixed point theorems on two or three metric spaces have been demonstrated. By applying contractive condition of integral type for class of weakly compatible maps in uncompleted intuitionistic fuzzy metric spaces without considering any continuous mappings, in this paper, we verify some frequent fixed point theorems for different mappings.