Fixed point theorems and Cauchy sequences in fuzzy metric spaces
type: Item
instance of: scholarly article
title: Fixed point theorems and Cauchy sequences in fuzzy metric spaces
zbMATH Open document ID: 1029.54012
DOI: 10.1016/S0165-0114(02)00132-X
author: R. Vasuki
author: P. Veeramani
published in: Fuzzy Sets and Systems
publication date: 2003-05-22T00:00:00Z
review text: One can find several definitions of the concept of a Cauchy sequence in a fuzzy metric space in the sense of Kramosil and Michalek. This paper presents an example illustrating that definitions given by \textit{M. Grabiec} [ibid. 27, 385-389 (1989; Zbl 0664.54032)] and \textit{R. Vasuki} [ibid. 97, 395-397 (1998; Zbl 0960.54005)] are not equivalent to the definition of George and Veeramani. This fact explains in particular why ``fixed point type'' theorems proved by different authors (see e.g., papers by M. Grabiec, V. Gregori and A. Sapena and R. Vasuki) sometimes have a different ``shape''.
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 54E35
zbMATH DE Number: 1915170
zbMATH Keywords: Fuzzy metric space
zbMATH Keywords: Cauchy sequence
zbMATH Keywords: Fixed point theorems
reviewed by: Alexander Šostak
MaRDI profile type: Publication
cites work: On some results in fuzzy metric spaces
cites work: Fixed points in fuzzy metric spaces
cites work: On fixed-point theorems in fuzzy metric spaces
cites work: Comments on `A common fixed point theorem in a fuzzy metric space'
cites work: A common fixed point theorem in a fuzzy metric space
full work available at URL: s0165-0114(02)00132-x
OpenAlex ID: W2011977682
description: scientific article; zbMATH DE number 1915170