Fuzzy Metric Spaces Research Articles

Fixed point theory for cyclic $varphi$-contractions in fuzzy metric spaces

In this paper, the notion of cyclic $varphi$-contraction in fuzzymetric spaces is introduced and a fixed point theorem for this typeof mapping is established. Meantime, an example is provided toillustrate this theorem. The main result shows that a self-mappingon a G-complete fuzzy metric space has a unique fixed point if itsatisfies the cyclic $varphi$-contraction. Afterwards, some results inconnection with the fixed point are given.

(ψ,α,β)-weak contraction in fuzzy metric spaces

The aim of this paper is to establish some new common fixed point theorems for mappings employing -weak contraction in fuzzy metric spaces. Our results generalize and improve various well known comparable results

Fixed Point Theorems For Weakly Compatible Maps Under E.a. Property In Fuzzy 2-metric Spaces

In this paper, we introduce E.A. property on fuzzy 2-metric spaces and prove common fixed point theorem for a pair of weakly compatible maps under E.A. property on fuzzy 2-metric spaces.

Nonlinear contractions and semigroups in complete fuzzy metric spaces

AbstractOur main purpose in this paper is to introduce the notion of φ -contractive mapping in fuzzy metric spaces and to present two new re-sults on the existence and the approximation of fixed point of nonlinearcontractions mappings and semigroups in fuzzy metric spaces. Theseresults are of interest in view of analogous results in metric spaces (seefor example [1], [7]) Mathematics Subject Classification: Primary 47H10, 54H25Keywords: Fixed point, fuzzy metric, left reversible semigroup, nonlinearcontractive conditions 1 Introduction Our terminology and notation for fuzzy metric spaces conform of that Georgeet al. [5, 6]. Recently Gregori et al. [4] have showed that the study of theintuitionistic fuzzy metric space (IFMS) ( X,M,N,∗,♦ ) can be reduced to thestudy of the fuzzy metric space (FMS) ( X,M,∗ ). More exactly, the topology τ ( MN ) of an IFMS ( X,M,N,∗,♦ ) coincides with the topology τ ( M ) generatedby the FMS ( X,M,∗ ), which has as a base the family of open sets. So, ourstudy is limited to FMSs.Definition 1.1

Common fixed points for R-weakly commuting mappings in fuzzy 2-metric spaces

The present paper extended a common fixed point theorem due to Vasuki (9) in fuzzy 2-metric spaces.

A common fixed point theorem in fuzzy 2-metric space

A common fixed point theorem in fuzzy 2-metric space

Common fixed point theorems for occasionally weakly compatible mappings in Menger spaces and applications

In 2008, Al-Thaga and Shahzad [Generalized I-nonexpansive self-maps and invariant approximations, Acta Math. Sinica 24(5) (2008), 867{876]introduced the notion of occasionally weakly compatible mappings (shortly owcmaps) which is more general than all the commutativity concepts. In the presentpaper, we prove common xed point theorems for families of owc maps in Mengerspaces. As applications to our results, we obtain the corresponding xed pointtheorems in fuzzy metric spaces. Our results improve and extend the results ofKohli and Vashistha [Common xed point theorems in probabilistic metric spaces,Acta Math. Hungar. 115(1-2) (2007), 37-47], Vasuki [Common xed points forR-weakly commuting maps in fuzzy metric spaces, Indian J. Pure Appl. Math.30 (1999), 419{423], Chugh and Kumar [Common xed point theorem in fuzzymetric spaces, Bull. Cal. Math. Soc. 94 (2002), 17{22] and Imdad and Ali [Somecommon xed point theorems in fuzzy metric spaces, Math. Commun. 11(2)(2006), 153-163].

Common fixed points for weak compatible maps in fuzzy metric spaces

In this note we shall prove common fixed point theorems for four mappings under weak compatible condition in the setting of fuzzy metric space, fuzzy 2-metric space, and fuzzy 3-metric spaces. Our results generalize the results of Singh, Jain and Jain.

Some Fixed Point Theorems for a Pair of Asymptotically Regular and Compatible Mappings in Fuzzy 2-Metric Space

In this paper we use the concept of a pair of asymptotically regular and compatible mappings to prove some common fixed point theorems in a complete fuzzy 2-metric space.

RELATION BETWEEN METRIC AND FUZZY METRIC SPACES AND SOME FIXED POINT THEOREMS

In this work we have considered several common fixed point results in metric spaces for weak compatible mappings. By applications of these results we establish some fixed point theorems in fuzzy metric spaces.

Some Fixed Point Theorems in Fuzzy Metric Spaces

In present paper we prove fixed point theorems in fuzzy metric space and then extend the result to fuzzy 2-metric and fuzzy 3-metric spaces. Our results generalize some well-known existing results.

Intuitionistic Fuzzy 2-Metric Space and Some Topological Properties

The notion of intuitionistic fuzzy metric space was introduced by Park (2004) and the concept of intuitionistic fuzzy normed space by Saadati and Park (2006). Recently Mursaleen and Lohani introduced the concept of intuitionistic fuzzy 2-metric space (2009) and intuitionistic fuzzy 2-norm space. This paper studies precompactness and metrizability in this new setup of intuitionistic fuzzy 2-metric space.

COMMON FIXED POINT THEOREMS FOR TWO MAPPINGS IN $\mathcal{M}$-FUZZY METRIC SPACES

In this paper, we prove some common fixed point theorem for two nonlinear mappings in complete -fuzzy metric spaces. Our main results improved versions of several fixed point theorems in complete fuzz metric spaces.

Common fixed point theorems for weakly compatible hybrid mappings

The purpose of this paper is to study common fixed point theorems for set-valued and single-valued mappings in fuzzy metric and fuzzy 2-metric spaces. Also, we give an example to support our theorem. Generalizations and extensions of known results are thereby obtained. In particular, theorems by Pathak and Singh (2007), Sharma and Tiwari (2005) and Som (1985).

Baire’s and Cantor’s theorems in intuitionistic fuzzy 2-metric spaces

Recently, Mursaleen, Lohani and Mohiuddine [Chaos Solitons & Fractals (2009), accepted] have introduced the notions of intuitionistic fuzzy 2-metric space. In this paper, we study various topological properties and prove Baire’s Theorem and Cantor’s Intersection Theorem in this new setup.

Intuitionistic fuzzy 2-metric space and its completion

Recently, Mursaleen and Lohani [Mursaleen M, Lohani Danish. Intuitionistic fuzzy 2-normed space and some related concepts. Chaos, Solitons & Fractals (2008), doi:10.1016/j.chaos.2008.11.006] have introduced the concept of intuitionistic fuzzy 2-normed space. In this paper, we introduce the concept of intuitionistic fuzzy 2-metric space and study its completion.

Semicompatibility and fixed point theorems in fuzzymetric space using implicit relation

The concept of semicompatibility has been introduced in fuzzy metric space and it has been applied to prove results on existence of unique common fixed point of four self‐maps satisfying an implicit relation. Recently, Popa (2002) has employed a similar but not the same implicit relation to obtain a fixed point theorem for d‐complete topological spaces. All the results of this paper are new.