Next Article in Journal
Role of Media and Effects of Infodemics and Escapes in the Spatial Spread of Epidemics: A Stochastic Multi-Region Model with Optimal Control Approach
Previous Article in Journal
Cayley Inclusion Problem Involving XOR-Operation
Previous Article in Special Issue
Fixpointed Idempotent Uninorm (Based) Logics
Article Menu
Issue 3 (March) cover image

Export Article

Open AccessArticle
Mathematics 2019, 7(3), 303;

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
(This article belongs to the Special Issue Fuzziness and Mathematical Logic)
PDF [296 KB, uploaded 25 March 2019]


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. View Full-Text
Keywords: fuzzy metric space; fuzzy contractive mapping; fixed point fuzzy metric space; fuzzy contractive mapping; fixed point
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Gregori, V.; Miñana, J.-J.; Miravet, D. Extended Fuzzy Metrics and Fixed Point Theorems. Mathematics 2019, 7, 303.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Mathematics EISSN 2227-7390 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top