Common fixed points of compatible maps in fuzzy metric spaces
type: Item
instance of: scholarly article
title: Common fixed points of compatible maps in fuzzy metric spaces
zbMATH Open document ID: 0985.54009
DOI: 10.1016/S0165-0114(98)00099-2
author: Bijendra Singh
author: M. S. Chauhan
published in: Fuzzy Sets and Systems
publication date: 2002-05-27T00:00:00Z
review text: Several researchers have defined the concept of fuzzy metric space in various ways. In this paper, the authors introduce the concept of compatibility on fuzzy metric space (in the sense of a definition given in [\textit{A. George} and the reviewer, ibid. 64, No. 3, 395-399 (1994; Zbl 0843.54014)] and use it to prove common fixed point theorems for compatible mappings. It should be noted that the authors prove two common fixed point theorems for a fuzzy metric space having continuous \(t\)-norm defined by \(a^*b= \min\{a,b\}\), \(a,b\in [0,1]\). The authors do not discuss their results for an arbitrary continuous \(t\)-norm. It is of worth to investigate whether the fixed point theorems proved in this paper are true for arbitrary \(t\)-norms.
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 54H25
zbMATH DE Number: 1545767
reviewed by: P. Veeramani
MaRDI profile type: Publication
cites work: On some results in fuzzy metric spaces
cites work: Compatible mapping and common fixed points
cites work: Compatible mappings and common fixed points. II
cites work: Fuzzy sets
Wikidata QID: Q127641634
full work available at URL: s0165-0114(98)00099-2
OpenAlex ID: W2081686977
description: scientific article; zbMATH DE number 1545767