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Some Remarks on Fuzzy sb -Metric Spaces

Author

Listed:
  • Tarkan Öner

    (Department of Mathematics, Muğla Sıtkı Koçman University, Muğla 48000, Turkey
    These authors contributed equally to this work.)

  • Alexander Šostak

    (Institute of Mathematics and CS and Department of Mathematics, University of Latvia, LV-1586 Riga, Latvia
    These authors contributed equally to this work.)

Abstract

Fuzzy strong b -metrics called here by fuzzy sb-metrics, were introduced recently as a fuzzy version of strong b -metrics. It was shown that open balls in fuzzy s b -metric spaces are open in the induced topology (as different from the case of fuzzy b -metric spaces) and thanks to this fact fuzzy s b -metrics have many useful properties common with fuzzy metric spaces which generally may fail to be in the case of fuzzy b -metric spaces. In the present paper, we go further in the research of fuzzy s b -metric spaces. It is shown that the class of fuzzy s b -metric spaces lies strictly between the classes of fuzzy metric and fuzzy b -metric spaces. We prove that the topology induced by a fuzzy s b -metric is metrizable. A characterization of completeness in terms of diameter zero sets in these structures is given. We investigate products and coproducts in the naturally defined category of fuzzy s b -metric spaces.

Suggested Citation

  • Tarkan Öner & Alexander Šostak, 2020. "Some Remarks on Fuzzy sb -Metric Spaces," Mathematics, MDPI, vol. 8(12), pages 1-19, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2123-:d:452052
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    References listed on IDEAS

    as
    1. Poom Kumam & Nguyen Van Dung & Vo Thi Le Hang, 2013. "Some Equivalences between Cone -Metric Spaces and -Metric Spaces," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, October.
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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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