Extended Fuzzy Metrics and Fixed Point Theorems
In this paper, we study those fuzzy metrics M on X, in the George and Veeramani's sense, such that t>0M(x,y,t)>0. The continuous extension M0 of M to X2x0,+infinity is called extended fuzzy metric. We prove that M0 generates a metrizable topology on X, which can be described in a similar...
| Autores: | , , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2019 |
| País: | España |
| Recursos: | Conselleria de Salut i Consum del Govern de les Illes Balears |
| Repositório: | Docusalut |
| Idioma: | inglês |
| OAI Identifier: | oai:docusalut.com:20.500.13003/17578 |
| Acesso em linha: | https://hdl.handle.net/20.500.13003/17578 |
| Access Level: | Acceso aberto |
| Palavra-chave: | fuzzy metric space fuzzy contractive mapping fixed point |
| Resumo: | In this paper, we study those fuzzy metrics M on X, in the George and Veeramani's sense, such that t>0M(x,y,t)>0. The continuous extension M0 of M to X2x0,+infinity is called extended fuzzy metric. We prove that M0 generates a metrizable topology on X, which can be described in a similar way to a classical metric. M0 can be used for simplifying or improving questions concerning M; in particular, we expose the interest of this kind of fuzzy metrics to obtain generalizations of fixed point theorems given in fuzzy metric spaces. |
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