New generalized fuzzy metrics and fixed point theorem in fuzzy metric space

In this paper, in fuzzy metric spaces (in the sense of Kramosil and Michalek (Kibernetika 11:336-344, 1957)) we introduce the concept of a generalized fuzzy metric which is the extension of a fuzzy metric. First, inspired by the ideas of Grabiec (Fuzzy Sets Syst. 125:385-389, 1989), we define a new G-contraction of Banach type with respect to this generalized fuzzy metric, which is a generalization of the contraction of Banach type (introduced by M Grabiec). Next, inspired by the ideas of Gregori and Sapena (Fuzzy Sets Syst. 125:245-252, 2002), we define a new GV-contraction of Banach type with respect to this generalized fuzzy metric, which is a generalization of the contraction of Banach type (introduced by V Gregori and A Sapena). Moreover, we provide the condition guaranteeing the existence of a fixed point for these single-valued contractions. Next, we show that the generalized pseudodistance J:X×X→[0,∞) (introduced by Włodarczyk and Plebaniak (Appl. Math. Lett. 24:325-328, 2011)) may generate some generalized fuzzy metric NJ on X. The paper includes also the comparison of our results with those existing in the literature

Fixed Point Results In Fuzzy Menger Space With Rational Expression

This paper presents some common fixed point theorems for occasionally weakly compatible mappings with rational expression in Fuzzy menger metric spaces. Keywords: Occasionally weakly compatible mappings, Fuzzy menger metric space,Weak compatible mapping, Semi-compatible mapping, Implicit function, common fixed point. Subject Classification: AMS (2000) 47H2

Multivalued generalizations of fixed point results in fuzzy metric spaces

This paper attempts to prove fixed and coincidence point results in fuzzy metric space using multivalued mappings. Altering distance function and multivalued strong {bn}-fuzzy contraction are used in order to do that. Presented theorems are generalization of some well known single valued results. Two examples are given to support the theoretical results

Common Fixed Point Theorems for Four Self Maps on A Menger Space, Satisfying Common E. A. Property

In this paper, we prove common fixed point theorems for four self maps by using weak compatibility in Menger spaces. Our result extend, generalized several fixed point theorems on Menger spaces. Keywords— Common fixed points, Metric space, Menger space, weak compatible mappings and E. A. property. AMS subject classification– 47H10, 54H25

Set-valued mappings in partially ordered fuzzy metric spaces

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Common fixed theorems for weakly compatible mappings via an implicit relation using the common (E.A) property in intuitionistic fuzzy metric spaces

In this chapter, we prove two common fixed theorems for weakly compatible mappings via an implicit relation using the common (E.A) property in intuitionistic fuzzy metric space

Common coupled fixed point theorems for contractive mappings 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 result. The result is a genuine generalization of the corresponding result of S.Sedghi et al. (2010).   Keywords: Fuzzy metric space, t-norm, g-convergent, coupled common fixed point. 2010 MSC: Primary 54E70; Secondary 54H25