Common fixed point theorems for hybrid pairs of maps in fuzzy metric spaces

M.A Ahmed,H.A Nafadi

doi:10.1016/j.joems.2013.10.006

Abstract

The purpose of this paper is to introduce the notion of common limit range property (CLR property) for two hybrid pairs of mappings in fuzzy metric spaces, and we prove common fixed point theorems using (CLR) property for these mappings with implicit relation. Our results extend some known results to multi-valued arena. Also, we prove common fixed point theorem in fuzzy metric spaces satisfying an integral type.

Highlights

The evolution of fuzzy mathematics solely banks on the notion of fuzzy set which was introduced by Zadeh [1] in 1965 with a view to represent the vagueness in everyday life
The feasible method of resolving such problems is the use of fuzzy sets (e.g. [2])
George and Veeramani [5] modified the concept of fuzzy metric space introduced by Kramosil and Michalek [6] with a view to obtain a Hausdorff topology on fuzzy metric spaces and this has recently found very fruitful applications in quantum particle physics in string theory and ε∞ theory (e.g. [7] and references cited therein)

Summary

Introduction

The evolution of fuzzy mathematics solely banks on the notion of fuzzy set which was introduced by Zadeh [1] in 1965 with a view to represent the vagueness in everyday life.

Objectives

Results

Conclusion