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Extended Fuzzy Metrics and Fixed Point Theorems

Author

Listed:
  • 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)

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.

Suggested Citation

  • Valentín Gregori & Juan-José Miñana & David Miravet, 2019. "Extended Fuzzy Metrics and Fixed Point Theorems," Mathematics, MDPI, vol. 7(3), pages 1-14, March.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:3:p:303-:d:216968
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    Citations

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    Cited by:

    1. Şuara Onbaşıoğlu & Banu Pazar Varol, 2023. "Intuitionistic Fuzzy Metric-like Spaces and Fixed-Point Results," Mathematics, MDPI, vol. 11(8), pages 1-15, April.

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