An identification theorem for the completion of the Hausdorff fuzzy metric

We prove that given a fuzzy metric space (in the sense of Kramosil and Michalek), the completion of its Hausdorff fuzzy metric space is isometric to the Hausdorff fuzzy metric space of its completion, when the Hausdorff fuzzy metrics are defined on the respective collections of non-empty closed subs...

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Detalles Bibliográficos
Autores: Gutierrez García, Javier, Sanchis, M., Romaguera Bonilla, Salvador|||0000-0001-7857-6139
Tipo de recurso: artículo
Fecha de publicación:2013
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:10251/43720
Acceso en línea:https://riunet.upv.es/handle/10251/43720
Access Level:acceso abierto
Palabra clave:Hausdorff fuzzy metric
Completion
Isometry
Contraction
Dynamical system
MATEMATICA APLICADA
Descripción
Sumario:We prove that given a fuzzy metric space (in the sense of Kramosil and Michalek), the completion of its Hausdorff fuzzy metric space is isometric to the Hausdorff fuzzy metric space of its completion, when the Hausdorff fuzzy metrics are defined on the respective collections of non-empty closed subsets. As a consequence, we deduce the corresponding result for metric spaces by using the standard fuzzy metric. An application to the extension of multivalued mappings and some illustrative examples are also given.