Common fixed point theorems in complete fuzzy metric spaces

Abstract

In this paper, common fixed point theorems for fuzzy maps in fuzzy metric spaces are proved. These theorems are fuzzy version of some known results in ordinary metric spaces.

A Common Fixed Point Theorem in Metric Space under General Contractive Condition

“…Some illustrative examples are furnished to highlight the realized improvements. Our result improves the main result of Sedghi and Shobe (2007).…”

“…Definition 5 (see [32]). By ⬦ : R + ×R + → R + , a binary operation will be denoted, satisfying the following conditions:…”

“…(1) ⬦ is associative and commutative, Definition 6 (see [32]). The binary operation ⬦ is said to satisfy -property if there exists a positive real number such that…”

“…In 2007, Sedghi and Shobe [32] proved a common fixed point theorem for weakly compatible mappings satisfying a new general contractive type condition. The aim of this paper is to prove a common fixed point theorem for two pairs of self-mappings by using the notions of compatibility and subsequential continuity (alternately subcompatibility and reciprocal continuity) satisfying general contractive condition in a metric space.…”

“…see[32, Theorem 2.1]). Let ( , ) be a complete metric space such that ⬦ satisfies the -property with > 0.…”