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A Characterization of Strong Completeness in Fuzzy Metric Spaces

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dc.contributor.authorGregori, Valentin
dc.contributor.authorMinana, Juan-Jose
dc.contributor.authorRoig, Bernardino
dc.contributor.authorSapena, Almanzor
dc.date.accessioned2024-09-13T09:14:43Z
dc.date.available2024-09-13T09:14:43Z
dc.date.issued2020-06
dc.description.abstractHere, we deal with the concept of fuzzy metric space(X,M,*), due to George and Veeramani. Based on the fuzzy diameter for a subset ofX, 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.en
dc.description.sponsorshipJuan-Jose Minana acknowledges financial support from FEDER/Ministerio de Ciencia, Innovacion y Universidades-Agencia Estatal de Investigacion/Proyecto PGC2018-095709-B-C21, and by Spanish Ministry of Economy and Competitiveness under contract DPI2017-86372-C3-3-R (AEI, FEDER, UE). This work was also partially supported by Programa Operatiu FEDER 2014-2020 de les Illes Balears, by project PROCOE/4/2017 (Direccio General d'Innovacio i Recerca, Govern de les Illes Balears), and by projects ROBINS and BUGWRIGHT2. These two latest projects have received funding from the European Union's Horizon 2020 research and innovation program under grant agreements Nos. 779776 and 871260, respectively. This publication reflects only the authors views and the European Union is not liable for any use that may be made of the information contained therein.es_ES
dc.format.number6es_ES
dc.format.page861es_ES
dc.format.volume8es_ES
dc.identifier.citationGregori V, Minana JJ, Roig B, Sapena A. A Characterization of Strong Completeness in Fuzzy Metric Spaces. Mathematics. 2020 Jun;8(6):861.en
dc.identifier.doi10.3390/math8060861
dc.identifier.e-issn2227-7390es_ES
dc.identifier.journalMathematicses_ES
dc.identifier.otherhttps://hdl.handle.net/20.500.13003/19400
dc.identifier.scopus2-s2.0-85087067491
dc.identifier.urihttps://hdl.handle.net/20.500.12105/22968
dc.identifier.wos553515900001
dc.language.isoengen
dc.publisherMultidisciplinary Digital Publishing Institute (MDPI)
dc.relation.publisherversionhttps://dx.doi.org/10.3390/math8060861en
dc.rights.accessRightsopen accessen
dc.rights.licenseAttribution 4.0 International*
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/*
dc.subjectFuzzy metric
dc.subjectCauchy sequence
dc.subject(strong) convergence
dc.subjectCompleteness
dc.subjectFuzzy diameter
dc.titleA Characterization of Strong Completeness in Fuzzy Metric Spacesen
dc.typeresearch articleen
dspace.entity.typePublication
relation.isPublisherOfPublication30293a55-0e53-431f-ae8c-14ab01127be9
relation.isPublisherOfPublication.latestForDiscovery30293a55-0e53-431f-ae8c-14ab01127be9

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