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...

Descripción completa

Detalles Bibliográficos
Autores: Gregori, Valentin, Miñana, Juan-José, Miravet, David
Tipo de recurso: artículo
Fecha de publicación:2019
País:España
Institución:Conselleria de Salut i Consum del Govern de les Illes Balears
Repositorio:Docusalut
Idioma:inglés
OAI Identifier:oai:docusalut.com:20.500.13003/17578
Acceso en línea:https://hdl.handle.net/20.500.13003/17578
Access Level:acceso abierto
Palabra clave:fuzzy metric space
fuzzy contractive mapping
fixed point
Descripción
Sumario: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.