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On Metric-Type Spaces Based on Extended T -Conorms

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

Kirk and Shahzad introduced the class of strong b-metric spaces lying between the class of b-metric spaces and the class of metric spaces. As compared with b-metric spaces, strong b-metric spaces have the advantage that open balls are open in the induced topology and, hence, they have many properties that are similar to the properties of classic metric spaces. Having noticed the advantages of strong b-metric spaces Kirk and Shahzad complained about the absence of non-trivial examples of such spaces. It is the main aim of this paper to construct a series of strong b-metric spaces that fail to be metric. Realizing this programme, we found it reasonable to consider these metric-type spaces in the context when the ordinary sum operation is replaced by operation ⊕, where ⊕ is an extended t-conorm satisfying certain conditions.

Suggested Citation

  • Tarkan Öner & Alexander Šostak, 2020. "On Metric-Type Spaces Based on Extended T -Conorms," Mathematics, MDPI, vol. 8(7), pages 1-17, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1097-:d:380516
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