Extended Fuzzy Metrics and Fixed Point Theorems
Instituto de Investigación para la Gestión Integrada de Zonas Costeras, Universitat Politècnica de València, Campus de Gandia, Calle Paranimf 1, 46730 Gandia, Spain
Departament de Ciències Matemàtiques i Informàtica, Universitat de les Illes Balears, Carretera de Valldemossa km 7.5, 07122 Palma, Spain
Author to whom correspondence should be addressed.
Received: 31 December 2018 / Revised: 18 February 2019 / Accepted: 20 March 2019 / Published: 25 March 2019
PDF [296 KB, uploaded 25 March 2019]
In this paper, we study those fuzzy metrics M
, in the George and Veeramani’s sense, such that
. The continuous extension
is called extended fuzzy metric. We prove that
generates a metrizable topology on X
, which can be described in a similar way to a classical metric.
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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MDPI and ACS Style
Gregori, V.; Miñana, J.-J.; Miravet, D. Extended Fuzzy Metrics and Fixed Point Theorems. Mathematics 2019, 7, 303.
Gregori V, Miñana J-J, Miravet D. Extended Fuzzy Metrics and Fixed Point Theorems. Mathematics. 2019; 7(3):303.
Gregori, Valentín; Miñana, Juan-José; Miravet, David. 2019. "Extended Fuzzy Metrics and Fixed Point Theorems." Mathematics 7, no. 3: 303.
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