A Banach contraction principle in fuzzy metric spaces defined by means of t-conorms
[EN] 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...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/187700 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/187700 |
| Access Level: | acceso abierto |
| Palabra clave: | Fuzzy metric space Fuzzy contractive mapping Archimedean continuous t-conorm Fixed point K-contraction MATEMATICA APLICADA |
| Sumario: | [EN] 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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