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On metrization of fuzzy metrics and application to fixed point theory

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On metrization of fuzzy metrics and application to fixed point theory

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dc.contributor.author Miñana, Juan-José es_ES
dc.contributor.author ostak, Alexander es_ES
dc.contributor.author Valero, Oscar es_ES
dc.date.accessioned 2024-11-29T19:07:51Z
dc.date.available 2024-11-29T19:07:51Z
dc.date.issued 2023-09-30 es_ES
dc.identifier.issn 0165-0114 es_ES
dc.identifier.uri http://hdl.handle.net/10251/212488
dc.description.abstract [EN] It is a well-known fact that the topology induced by a fuzzy metric is metrizable. Nevertheless, the problem of how to obtain a classical metric from a fuzzy one in such a way that both induce the same topology is not solved completely. A new method to construct a classical metric from a fuzzy metric, whenever it is defined by means of an Archimedean t-norm, has recently been introduced in the literature. Motivated by this fact, we focus our efforts on such a method in this paper. We prove that the topology induced by a given fuzzy metric M and the topology induced by the metric constructed from M by means of such a method coincide. Besides, we prove that the completeness of the fuzzy metric space is equivalent to the completeness of the associated classical metric obtained by the aforementioned method. Moreover, such results are applied to obtain fuzzy versions of two well-known classical fixed point theorems in metric spaces, one due to Matkowski and the other one proved by Meir and Keeler. Although such theorems have already been adapted to the fuzzy context in the literature, we show an inconvenience on their applicability which motivates the introduction of these two new fuzzy versions. es_ES
dc.description.sponsorship A. Sostak is thankful to the University of Balearic Islands for the financial support for his stay during which this work was executed. This research was funded by Proyecto PGC2018-095709-B-C21 financiado por MCIN/AEI/10.13039/501100011033 y FEDER "Una manera de hacer Europa" and from project BUGWRIGHT2. This last project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreements No. 871260. 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.language Inglés es_ES
dc.publisher Elsevier es_ES
dc.relation.ispartof Fuzzy Sets and Systems es_ES
dc.rights Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) es_ES
dc.subject Fuzzy metric space es_ES
dc.subject Archimedean t-norm es_ES
dc.subject Additive generator es_ES
dc.subject Metrization es_ES
dc.subject Completeness es_ES
dc.subject Fixed point theorem es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title On metrization of fuzzy metrics and application to fixed point theory es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1016/j.fss.2023.108625 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-095709-B-C21/ES/METRICAS DIFUSAS Y OPERADORES DE INDISTINGUIBILIDAD: APLICACIONES EN ROBOTICA/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/EC/H2020/871260/EU/Autonomous Robotic Inspection and Maintenance on Ship Hulls and Storage Tanks/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Escuela Politécnica Superior de Gandia - Escola Politècnica Superior de Gandia es_ES
dc.description.bibliographicCitation Miñana, J.; Ostak, A.; Valero, O. (2023). On metrization of fuzzy metrics and application to fixed point theory. Fuzzy Sets and Systems. 468. https://doi.org/10.1016/j.fss.2023.108625 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.1016/j.fss.2023.108625 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 468 es_ES
dc.relation.pasarela S\501417 es_ES
dc.contributor.funder European Commission es_ES
dc.contributor.funder Universitat de les Illes Balears es_ES
dc.contributor.funder Agencia Estatal de Investigación es_ES
dc.contributor.funder European Regional Development Fund es_ES


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