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A Banach contraction principle in fuzzy metric spaces defined by means of t-conorms

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Abstract

Fixed point theory in fuzzy metric spaces has grown to become an intensive field of research. The difficulty of demonstrating a fixed point theorem in such kind of spaces makes the authors to demand extra conditions on the space other than completeness. In this paper, we introduce a new version of the celebrated Banach contracion principle in the context of fuzzy metric spaces. It is defined by means of t-conorms and constitutes an adaptation to the fuzzy context of the mentioned contracion principle more “faithful” than the ones already defined in the literature. In addition, such a notion allows us to prove a fixed point theorem without requiring any additional condition on the space apart from completeness. Our main result (Theorem 1) generalizes another one proved by Castro-Company and Tirado. Besides, the celebrated Banach fixed point theorem is obtained as a corollary of Theorem 1.

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Acknowledgements

Juan-José Miñana acknowledges financial support from FEDER/Ministerio de Ciencia, Innovación y Universidades-Agencia Estatal de Investigación/\(_{-}\)Proyecto PGC2018-095709-B-C21. This work is also partially supported by Programa Operatiu FEDER 2014-2020 de les Illes Balears, by project PROCOE/4/2017 (Direcció General d’Innovació 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 programme under grant agreements No 779776 and No 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.

Funding

Valentín Gregori acknowledges the support of Generalitat Valenciana under grant AICO-2020-136.

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Authors and Affiliations

  1. Instituto de Investigación para la Gestión Integrada de Zonas Costeras, Universitat Politècnica de València, Campus de Gandia, Calle Paranimf 1, 46730, Gandia, Spain

    Valentín Gregori

  2. Departament de Ciències Matemàtiques i Informàtica, Universitat de les Illes Balears, Carretera de Valldemossa km. 7.5, 07122, Palma, Spain

    Juan-José Miñana

  3. Institut d’Investigació Sanitària Illes Balears (IdISBa), Hospital Son Espases, 07120, Palma, Spain

    Juan-José Miñana

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  1. Valentín Gregori
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  2. Juan-José Miñana
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Correspondence to Valentín Gregori.

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Gregori, V., Miñana, JJ. A Banach contraction principle in fuzzy metric spaces defined by means of t-conorms. RACSAM 115, 129 (2021). https://doi.org/10.1007/s13398-021-01068-6

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