Common Coupled Fixed Point Theorems in Fuzzy Metric Spaces

Volume 5 Issue 4 October - December 2016

Research Paper

Common Coupled Fixed Point Theorems in Fuzzy Metric Spaces

T Rakesh Singh*, P Srikanth Rao**

* Associate Professor, Department of Mathematics, Aurora’s Technological Institute, Hyderabad, Telangana, India.

** Professor, Department of Mathematics, B. V. Raju Institute of Technology, Narsapur, Telangana, India.

Singh, T.R., and Rao, P.S. (2016). Common Coupled Fixed Point Theorems in Fuzzy Metric Spaces. i-manager’s Journal on Mathematics, 5(4), 1-10. https://doi.org/10.26634/jmat.5.4.8305

Abstract

A fuzzy set of X is a function with domain X and values in [0, 1]. If A is a fuzzy set and x ? X, then the function values A(x) are called the grade of membership of x in A. A mapping F from X to F(Y) is called a fuzzy mapping if for each x ? X; F(x) is a fuzzy set on Y and F(x)(y) denotes the degree of membership of y in F(x). Let X be a metric linear space and let W(X) denote the set of all fuzzy sets on X such that each of its α-cut is a nonempty compact and convex subset (approximate quantity) of X. A fuzzy mapping F from X to W(X) is called a fuzzy contraction mapping if there exists q ? (0, 1) such that D(F(x), F(y)) ≤ qd(x, y) for each x,y ? X. In this paper, two common coupled fixed point theorems for six self maps is proved under Wcompatible conditions in fuzzy metric spaces. Coupled fixed point and coupled point of coincidence for contractive mappings in complete fuzzy metric space is also obtained. The results obtain an extension of Theorem 2.1 by K. Pandu Ranga Rao, K. Rama Koteswara Rao, and S. Sedghi, (2014) [11]. Common Coupled Fixed Point Theorems in Fuzzy Metric Spaces. Finally, an example has been given to illustrate the usability of the main result.