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Characterizing Complete Fuzzy Metric Spaces Via Fixed Point Results

Author

Listed:
  • Salvador Romaguera

    (Instituto Universitario de Matemática Pura y Aplicada-IUMPA, Universitat Politècnica de València, 46022 Valencia, Spain)

  • Pedro Tirado

    (Instituto Universitario de Matemática Pura y Aplicada-IUMPA, Universitat Politècnica de València, 46022 Valencia, Spain)

Abstract

With the help of C-contractions having a fixed point, we obtain a characterization of complete fuzzy metric spaces, in the sense of Kramosil and Michalek, that extends the classical theorem of H. Hu (see “ Am. Math. Month. 1967, 74, 436–437”) that a metric space is complete if and only if any Banach contraction on any of its closed subsets has a fixed point. We apply our main result to deduce that a well-known fixed point theorem due to D. Mihet (see “ Fixed Point Theory 2005, 6, 71–78”) also allows us to characterize the fuzzy metric completeness.

Suggested Citation

  • Salvador Romaguera & Pedro Tirado, 2020. "Characterizing Complete Fuzzy Metric Spaces Via Fixed Point Results," Mathematics, MDPI, vol. 8(2), pages 1-7, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:273-:d:322172
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    Citations

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    Cited by:

    1. Reza Chaharpashlou & Reza Saadati & António M. Lopes, 2023. "Fuzzy Mittag–Leffler–Hyers–Ulam–Rassias Stability of Stochastic Differential Equations," Mathematics, MDPI, vol. 11(9), pages 1-11, May.
    2. Olga Grigorenko & Alexander Šostak, 2023. "Fuzzy Metrics in Terms of Fuzzy Relations," Mathematics, MDPI, vol. 11(16), pages 1-13, August.
    3. Salvador Romaguera, 2023. "Concerning Fuzzy b -Metric Spaces †," Mathematics, MDPI, vol. 11(22), pages 1-14, November.
    4. Olga Grigorenko & Alexander Šostak, 2022. "Fuzzy Extension of Crisp Metric by Means of Fuzzy Equivalence Relation," Mathematics, MDPI, vol. 10(24), pages 1-15, December.

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