Fixed Point Theorem in Fuzzy Metric Spaces Satisfying E.A Property

Vishal Gupta

doi:10.17485/ijst/2012/v5i12.14

Abstract

The present paper is an attempt to prove common fixed point theorem for six mappings in fuzzy metric spaces. Our main result extends and improves the strict contractive conditions on fuzzy metric spaces and establishes the existence of common fixed points for six mappings under general contractive condition of integral type by using E.A property. The concept of weak compatible mappings is also used to prove the desired result.

Highlights

The notion of a fuzzy set was introduced by (Zadeh, 1965)
Thereafter, it was developed extensively by (Schweizer & Sklar,1960), (Grabiec, 1988), (Murthy et al, 2010), (Bhatia et al.,2010) and many more authors. This theory includes interesting applications in diverse areas. (Aamri & Moutawakil, 2002) generalized the concept of non compatibility by defining the notion of E.A. Property and they proved common fixed point theorems under strict contractive conditions
Theorem 3.1: Let (X,M,*) be a fuzzy metric space with continuous t-norm defined by a*b= min {a, b} for all a,b in [0,1 ] and A, B, S, T, P and Q be mappings from X into itself such that

Summary

Introduction

The notion of a fuzzy set was introduced by (Zadeh, 1965) It brought a turning point in the development of mathematics and laid the foundation of fuzziness in mathematics. Thereafter, it was developed extensively by (Schweizer & Sklar ,1960), (Grabiec , 1988), (Murthy et al, 2010), (Bhatia et al.,2010) and many more authors. (Aamri & Moutawakil, 2002) generalized the concept of non compatibility by defining the notion of E.A property and they proved common fixed point theorems under strict contractive conditions.

Definitions

Main Result