Comment on: ``Common fixed point theorems for commutating mappings in fuzzy metric spaces''
type: Item
instance of: scholarly article
title: Comment on: ``Common fixed point theorems for commutating mappings in fuzzy metric spaces''
zbMATH Open document ID: 1256.54082
DOI: 10.1155/2012/142858
author: Yonghong Shen
author: Wei Chen
author: San-Fu Wang
published in: Abstract and Applied Analysis
publication date: 2013-02-04T00:00:00Z
review text: Summary: In a recent paper [ibid. 2012, Article ID 729758, 5 p. (2012; Zbl 1242.54032)], \textit{F. Zheng} and \textit{X. Lian} proved 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 in [loc. cit.] actually holds in an \(M\)-complete fuzzy metric space. Our results improve and extend some existing results in the relevant literature.
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 54A40
zbMATH DE Number: 6134021
Wikidata QID: Q58694925
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/142858
OpenAlex ID: W2052045433
cites work: Common fixed point theorems for commutating mappings in fuzzy metric spaces
cites work: Commuting Mappings and Fixed Points
cites work: Q4081991
cites work: On some results in fuzzy metric spaces
cites work: \(G\)-completeness and \(M\)-completeness in fuzzy metric spaces: a note on a common fixed point theorem
cites work: Q2996632
cites work: A common fixed point theorem in fuzzy metric spaces
cites work: The metrization of statistical metric spaces
cites work: Fixed points in fuzzy metric spaces
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description: scientific article; zbMATH DE number 6134021