Extended Fuzzy Metrics and Fixed Point Theorems

Valentín Gregori, Juan-José Miñana and David Miravet
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Valentín Gregori: Instituto de Investigación para la Gestión Integrada de Zonas Costeras, Universitat Politècnica de València, Campus de Gandia, Calle Paranimf 1, 46730 Gandia, Spain
Juan-José Miñana: Departament de Ciències Matemàtiques i Informàtica, Universitat de les Illes Balears, Carretera de Valldemossa km 7.5, 07122 Palma, Spain
David Miravet: Instituto de Investigación para la Gestión Integrada de Zonas Costeras, Universitat Politècnica de València, Campus de Gandia, Calle Paranimf 1, 46730 Gandia, Spain

Mathematics, 2019, vol. 7, issue 3, 1-14

Abstract: In this paper, we study those fuzzy metrics M on X , in the George and Veeramani’s sense, such that ? t > 0 M ( x , y , t ) > 0 . The continuous extension M 0 of M to X 2 × 0 , + ∞ is called extended fuzzy metric. We prove that M 0 generates a metrizable topology on X , which can be described in a similar way to a classical metric. M 0 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.

Keywords: fuzzy metric space; fuzzy contractive mapping; fixed point (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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