Mappings In Fuzzy Metric Spaces Research Articles

On Fuzzy "Equation missing" -Contractive Mappings in Fuzzy Metric Spaces

AbstractWe answer into affirmative an open question raised by A. Razani in 2005. An essential role in our proofs is played by the separation axiom in the definition of a fuzzy metric space in the sense of George and Veeramani.

Common fixed point theorems for multi-valued contractions

In this paper, a common fixed point theorem for weakly compatible maps in fuzzy metric spaces is proved. Mathematics Subject Classification: 54E40; 54E35; 54H25

On fixed degree theorems for fuzzy mappings in Menger PM-spaces

In this paper, we establish a new common fixed degree theorem for a sequence of fuzzy mappings in Menger PM-spaces. As an immediate consequence of this theorem, we obtain an improvement of a corresponding result of Chang et al. (Fuzzy Sets and Systems 87 (1997) 325–334). In addition, we also obtain some fixed degree and fixed point theorems for fuzzy mappings in fuzzy metric spaces. Our results unify and generalize the results of Heilpern (J. Math. Anal. Appl. 83 (1981) 566–569), Butnariu (Fuzzy Sets and Systems 7 (1982) 191–207), Hadžíc (Fuzzy Sets and Systems 29 (1989) 115–125), Fang (Fuzzy Sets and Systems 48 (1992) 391–395), Lee et al. (Fuzzy Sets and Systems 61 (1994) 309–312; J. Fuzzy Math. 2 (1994) 859–870) and Chang et al. (Math. Japon. 40 (1994) 289–293; Fuzzy Sets and Systems 87 (1997) 325–334).

On Fuzzy Metric Space

In this paper we prove a common fixed point theorem for three mappings in fuzzy metric space and then extend this result to fuzzy 2 and 3-metric spaces. Our theorem is an extension of result of Fisher [12], to fuzzy metric spaces.

Common fixed point theorems in fuzzy metric spaces

In this paper we prove common fixed point theorems for six mappings in fuzzy metric space. Our main results extend, generalize and fuzzify some known results in fuzzy metric spaces, probabilistic metric spaces and uniform spaces.

Common fixed points of compatible maps in fuzzy metric spaces

The purpose of this paper is to introduce the concept of compatibility in fuzzy metric space and prove two common fixed point theorems illustrating with an example.

Coincidence point theorems in generating spaces of quasi-metric family

In this paper, we establish some new versions of coincidence point theorems for single-valued and multi-valued mappings in generating spaces of quasi-metric family. As applications, we utilize our main theorems to prove coincidence point theorems and fixed point theorems for single-valued and multi-valued mappings in fuzzy metric spaces and probabilistic metric spaces.

An extension of Ekeland's variational principle in fuzzy metric space and its applications

An extension of Ekeland's variational principle in fuzzy metric space, which is an essential and the most general improvement of Ekeland's variational principle in fuzzy metric space up to now, is established. As an application, we obtain Caristi's coincidence theorem for set-valued mappings in fuzzy metric spaces. Further, a direct simple proof of the equivalence between the two theorems is given. Some applications of these results to probabilistic metric spaces are presented. All these results, even in usual metric space, are also the latest.

Coincidence point theorems and minimization theorems in fuzzy metric spaces

In this paper, some new versions of coincidence point theorems and minimization theorems for single-valued and multi-valued mappings in generating spaces of the quasi-metric family are obtained. As applications, we utilize our main theorems to prove coincidence point theorems, fixed point theorems and minimization theorems for single-valued and multi-valued mappings in fuzzy metric spaces and probabilistic metric spaces.

Coincidence theorems for set-valued mappings and Ekeland's variational principle in fuzzy metric spaces

In this paper, we establish a coincidence theorem for set-valued mappings in fuzzy metric spaces with a view to generalizing Downing-Kirk's fixed point theorem in metric spaces. As consequences, we obtain Caristi's coincidence theorem for set-valued mappings and a more general type of Ekeland's variational principle in fuzzy metric spaces. Further, we also give a direct simple proof of the equivalence between these two theorems in fuzzy metric spaces. Some applications of these results to probabilistic metric spaces are presented.

Fixed point theorems and variational principle in fuzzy metric space

Abstract The variational principle and fixed point theorems for singlevalued and multivalued mappings in fuzzy metric space are given and their equivalence is proved.

On fixed point theorems in fuzzy metric spaces

The purpose of this paper is to give some new fixed point theorems for contractive type mappings in fuzzy metric spaces. The results presented improve and generalize some recent results.

Fixed point theorems for multivalued mappings in some classes of fuzzy metric spaces

Using the probabilistic function of noncompactness a fixed point theorem for multivalued mappings in probabilistic metric spaces is proved. As an application a fixed point theorem for multivalued mappings in fuzzy metric spaces is obtained.

Common Fixed Point of Semi Compatible Maps in Fuzzy Metric Spaces

The purpose of this paper is to prove a common fixed point theorem on fuzzy metric space usingthe notion of semi compatibility, our result generalize the result of Som. Also, we are givingan example that make strong to our result.Keywords: Common fixed point; Fuzzy metric space; R-weakly commuting; Semi compatible maps.DOI: 10.3126/kuset.v6i1.3313 Kathmandu University Journal of Science, Engineering and Technology Vol.6(1) 2010, pp70-78