Common Fixed Point Theorems for Commutating Mappings in Fuzzy Metric Spaces

Abstract

We generalize Jungck's theorem in Jungck (1976) to fuzzy metric spaces and prove common fixed point theorems for commutative mappings in fuzzy metric spaces.

A Common Fixed Point Theorem in Fuzzy Metric Spaces with Nonlinear Contractive Type Condition Defined Using Φ-Function

“…Let and be R-weakly commuting self-mappings on , and let be continuous such that ( ) ⊆ ( ). Let, for all , ∈ and every > 0, ( ( ) , ( ) , ( )) ≥ ( ( ) , ( ) , ( )) (11) hold, where is a Φ-function and 0 < < 1. If there exists a point 0 ∈ and 0 ∈ N such that the set…”

“…Properties of fuzzy metric spaces and fixed point results in these spaces are obtained by several authors [4,[7][8][9][10][11]. Results presented in [10,11] consider the fixed point results for mappings satisfying nonlinear contractive type condition, but the class of fuzzy metric spaces is restrictive because the authors added an additional axiom for fuzzy metric spaces. Our result is applicable for arbitrary fuzzy metric space without restrictions.…”