Common Fixed Point Theorems in Compatible Mappings of Type (P*) of Generalized Intuitionistic Fuzzy Metric Spaces

Muthuraj R,Pandiselvi R

doi:10.5121/mathsj.2015.2301

Abstract

Common Fixed Point Theorems in Compatible Mappings of Type (P*) of Generalized Intuitionistic Fuzzy Metric Spaces

Highlights

The Concept of fuzzy set was introduced by Zadeh [23] in 1965 .Following the concept of fuzzy sets, Deng
[6] Kaleva and Seikalla [12] and kramosil and Michalek [13] introduced the concept of fuzzy metric space, George and Veeramani [7] modified the concept of fuzzy metric space introduced by kramosil and Michalek [13]
Using the idea of intuitionistic fuzzy sets Park [16] defined the notion of intuitionistic fuzzy metric space with the help of continuous t- norm and continuous t- conorm as a generalization of fuzzy metric space, George and Veeramani [8] had showed that every metric induces an intuitionistic fuzzy metric and found a necessary and sufficient conditions for an intuitionistic fuzzy metric space to be complete

Summary

Introduction

The Concept of fuzzy set was introduced by Zadeh [23] in 1965 .Following the concept of fuzzy sets, Deng [6] Kaleva and Seikalla [12] and kramosil and Michalek [13] introduced the concept of fuzzy metric space, George and Veeramani [7] modified the concept of fuzzy metric space introduced by kramosil and Michalek [13] .Further, Sedghi and Shobe [19] defined M-fuzzy metric space and proved a common fixed point theorem in it. 0. ASz = SSz. Let A and S self mappings from an intuitionistic fuzzy metric space (X, M, ࣨ, ∗, ◊) with t ∗ t ≥ t and (1- t) ◊ (1- t) ≤ 1- t for all t ∈ [0, 1] if the pair (A, S) are compatible of type (p -1) and Axn, Sxn → z for some z in X and a sequence {xn} in X.

Results

Conclusion