Common Fixed Point Theorems on Complete and Weak $G$-Complete Fuzzy Metric Spaces

TL;DR

This paper establishes new common fixed point theorems for pairs of mappings in complete and weak G-complete fuzzy metric spaces, extending and improving previous results with broader applicability.

Contribution

It introduces symmetric pairs of β-admissible mappings and generalizes existing fixed point theorems for fuzzy contractive mappings.

Findings

Generalized fixed point theorems for fuzzy metric spaces.

Rectified and extended previous fixed point results.

Provided non-trivial examples demonstrating applicability.

Abstract

Motivated by Gopal and Vetro [Iranian Journal of Fuzzy Systems, 11(3), 95-107], we introduce a symmetric pair of $\beta$-admissible mappings and obtain common fixed point theorems for such a pair in complete and weak $G$-complete fuzzy metric spaces. In particular, we rectified, generalize and improve the common fixed point theorem obtained by Turkoglu and Sangurlu [Journal of Intelligent & Fuzzy Systems, 26(1), 137-142] for two fuzzy $\psi$-contractive mappings. We include non-trivial examples to exhibit the generality and demonstrate our results.