Comment on “Common Fixed Point Theorems for Commutating Mappings in Fuzzy Metric Spaces”

Abstract

In the recent paper “common fixed point theorems for commutating mappings in fuzzy metric spaces,” the authors proved that a common fixed point theorem for commutating mappings in $G$-complete fuzzy metric spaces and gave an example to illustrate the main result. In this note, we point out that the above example is incorrect because it does not satisfy the condition of $G$-completeness, and then two appropriate examples are given. In addition, we prove that the theorem proposed by Zheng and Lian actually holds in an $M$-complete fuzzy metric space. Our results improve and extend some existing results in the relevant literature.