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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 142858, 7 pages
http://dx.doi.org/10.1155/2012/142858
Letter to the Editor

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

1School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, China
2School of Information, Capital University of Economics and Business, Beijing 100070, China

Received 3 August 2012; Accepted 17 October 2012

Copyright © 2012 Yonghong Shen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 -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 -completeness, and then two appropriate examples are given. In addition, we prove that the theorem proposed by Zheng and Lian actually holds in an -complete fuzzy metric space. Our results improve and extend some existing results in the relevant literature.