Conditions In Fuzzy Metric Spaces Research Articles

Rational Type Fuzzy-Contraction Results in Fuzzy Metric Spaces with an Application

This paper aims to introduce the new concept of rational type fuzzy-contraction mappings in fuzzy metric spaces. We prove some fixed point results under the rational type fuzzy-contraction conditions in fuzzy metric spaces with illustrative examples to support our results. This new concept will play a very important role in the theory of fuzzy fixed point results and can be generalized for different contractive type mappings in the context of fuzzy metric spaces. Moreover, we present an application of a nonlinear integral type equation to get the existing result for a unique solution to support our work.

Some Fixed Point Theorems of Ćirić Type in Fuzzy Metric Spaces

The main aim of the current paper is the investigation of possibilities for improvements and generalizations contractive condition of Ćirić in the fuzzy metric spaces. Various versions of fuzzy contractive conditions are studied in two directions. First, motivated by recent results, more general contractive conditions in fuzzy metric spaces are achieved and secondly, quasi-contractive type of mappings are investigated in order to obtain fixed point results with a wider class of t-norms.

Common Fixed Point Theorems Under Strict Contractive Conditions in Fuzzy Metric Spaces

Fuzzy sets originally introduced Zadeh. Using Concept of fuzzy sets, various theories regarding giving new concepts of fuzzy metric spaces were considered by various authors. After that, many authors have studied fixed point theory in such spaces and proved various fixed point theorems in such spaces. In 1975, Kramosilet al. have introduced the concept of fuzzy metric spaces. In this paper, using concept of fuzzy metric space given by Kramosil et al., we prove common fixed point theorems for weakly compatible mappings satisfying strict contractive condition in fuzzy metric spaces by using property (E.A). Our proved results generalize known fixed point theorems in literature. We prove two common fixed point theorems in this paper, one for four maps and other one for two maps. Mathematics subject classification: 54E40, 54E35, 54H25.

Common Fixed Point Theorem in Fuzzy Metric Spaces using weakly compatible maps

The aim of this paper is to prove a common fixed theorem for four mappings under weakly compatible condition in fuzzy metric space. While proving our results we utilize the idea of weakly compatible maps due to Jungck and Rhoades. Our results substantially generalize and improve a multitude of relevant common fixed point theorems of the existing literature in metric as well as fuzzy metric space.

Existence and uniqueness of a common fixed point under a limit contractive condition

Abstract In this paper, utilizing the notion of common limit range property for two pairs of self mappings, we prove common fixed point theorems in fuzzy metric spaces under a limit contractive condition, which improve and extend the results of Zhu et al. [Common fixed point theorems of new contractive conditions in fuzzy metric spaces, J. Appl. Math. 2013:145190, 2013]. We also give some examples to demonstrate the validity of the hypotheses of our results. As an application to our main result, we obtain a fixed point theorem for four finite families of self mappings in fuzzy metric space. MSC: 47H10, 54H25.

Common coupled fixed point theorems for weakly compatible mappings in fuzzy metric spaces

In this paper, we prove a common fixed point theorem for weakly compatible mappings under ϕ-contractive conditions in fuzzy metric spaces. We also give an example to illustrate the theorem. The result is a genuine generalization of the corresponding result of Hu (Fixed Point Theory Appl. 2011:363716, 2011, doi:10.1155/2011/363716). We also indicate a minor mistake in Hu (Fixed Point Theory Appl. 2011:363716, 2011, doi:10.1155/2011/363716).

Common Fixed Point Theorems of New Contractive Conditions in Fuzzy Metric Spaces

Some new limit contractive conditions in fuzzy metric spaces are introduced, by using property (E.A), some common fixed point theorems for four maps are proved in GV-fuzzy metric spaces. As an application of our results, some new contractive conditions are presented, and some common fixed point theorems are proved under these contractive conditions. The contractive conditions presented in this paper contain or generalize many contractive conditions that appeared in the literatures. Some examples are given to illustrate that our results are real generalizations for the results in the references and to show that our limit contractive conditions are important for the existence of fixed point.

COMMON FIXED POINT THEOREMS UNDER STRICT CONTRACTIVE CONDITIONS IN FUZZY METRIC SPACES USING PROPERTY (E.A)

We prove common fixed point theorems for weakly compatible mappings satisfying strict contractive conditions in fuzzy metric spaces using property (E.A). Our theorems extend a theorem of [1].

Common Coupled Fixed Point Theorems for Contractive Mappings in Fuzzy Metric Spaces

AbstractWe prove a common fixed point theorem for mappings under "Equation missing"-contractive conditions in fuzzy metric spaces. We also give an example to illustrate the theorem. The result is a genuine generalization of the corresponding result of S.Sedghi et al. (2010)