On fixed-point theorems in fuzzy metric spaces
type: Item
instance of: scholarly article
title: On fixed-point theorems in fuzzy metric spaces
zbMATH Open document ID: 0995.54046
DOI: 10.1016/S0165-0114(00)00088-9
author: Valentín Gregori
author: Almanzor Sapena
published in: Fuzzy Sets and Systems
publication date: 2002-05-21T00:00:00Z
review text: The authors have attempted to extend the Banach fixed point theorem to fuzzy contractive mappings on different types of complete fuzzy metric spaces. They have also introduced a uniform structure on the fuzzy metric space introduced in [\textit{A. George} and \textit{P. Veeramani}, ibid. 64, No. 3, 395-399 (1994; Zbl 0843.54014)]. The authors have proved fuzzy Banach contraction theorems in the sense of complete fuzzy metric space introduced in [\textit{A. George} and \textit{P. Veeramani}, loc. cit.] and in the sense of fuzzy completeness given by \textit{M. Grabiec} [ibid. 27, No. 3, 385-389 (1988; Zbl 0664.54032)]. They have also introduced a notion called fuzzy contractive sequence and observed that every fuzzy contractive sequence is G-Cauchy (definition of Cauchy sequence as given in Grabiec) and ask the question: Is a fuzzy contractive sequence a Cauchy sequence (in this case the definition of Cauchy sequence should be taken as given in [A. George and P. Veeramani, loc. cit.].
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 54A40
zbMATH DE Number: 1743130
zbMATH Keywords: Banach fixed point theorem
zbMATH Keywords: Banach contraction theorems
zbMATH Keywords: fuzzy contractive sequence
zbMATH Keywords: Cauchy sequence
reviewed by: P. Veeramani
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1743130