A characterization of strong completeness in fuzzy metric spaces

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dc.contributor.author Gregori, Valentín
dc.contributor.author Miñana, Juan José
dc.contributor.author Roig, Bernardino
dc.contributor.author Sapena, Almanzor
dc.date.accessioned 2020-05-29T06:46:08Z
dc.date.available 2020-05-29T06:46:08Z
dc.identifier.uri http://hdl.handle.net/11201/152645
dc.description.abstract [eng] Here, we deal with the concept of fuzzy metric space (X,M,*) , due to George and Veeramani. Based on the fuzzy diameter for a subset of X , we introduce the notion of strong fuzzy diameter zero for a family of subsets. Then, we characterize nested sequences of subsets having strong fuzzy diameter zero using their fuzzy diameter. Examples of sequences of subsets which do or do not have strong fuzzy diameter zero are provided. Our main result is the following characterization: a fuzzy metric space is strongly complete if and only if every nested sequence of close subsets which has strong fuzzy diameter zero has a singleton intersection. Moreover, the standard fuzzy metric is studied as a particular case. Finally, this work points out a route of research in fuzzy fixed point theory.
dc.format application/pdf
dc.relation.isformatof https://doi.org/10.3390/math8060861
dc.relation.ispartof Mathematics, 2020, vol. 8, num. 6, p. 1-11
dc.rights , 2020
dc.subject.classification Matemàtica
dc.subject.classification 004 - Informàtica
dc.subject.other Mathematics
dc.subject.other 004 - Computer Science and Technology. Computing. Data processing
dc.title A characterization of strong completeness in fuzzy metric spaces
dc.type info:eu-repo/semantics/article
dc.date.updated 2020-05-29T06:46:08Z
dc.subject.keywords Fuzzy metric space
dc.subject.keywords Cauchy sequence
dc.subject.keywords strong convergence
dc.subject.keywords Completeness
dc.subject.keywords fuzzy diameter
dc.rights.accessRights info:eu-repo/semantics/openAccess
dc.identifier.doi https://doi.org/10.3390/math8060861

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