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Pre-Symmetric w -Cone Distances and Characterization of TVS-Cone Metric Completeness

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  • Seyedeh Sara Karimizad

    (Department of Mathematics, Faculty of Basic Sciences, Ilam University, Ilam P.O. Box 69315-516, Iran)

  • Ghasem Soleimani Rad

    (Young Researchers and Elite Club, Islamic Azad University, Tehran P.O. Box 14778-93855, Iran)

Abstract

Motivated by two definitions of distance, “pre-symmetric w -distance” and “ w -cone distance”, we define the concept of a pre-symmetric w -cone distance in a TVS-CMS and introduce its properties and examples. Also, we discuss the TVS-cone version of the recent results obtained by Romaguera and Tirado. Meanwhile, using Minkowski functionals, we show the equivalency between some consequences concerning a pre-symmetric w -distance in a usual metric space and a pre-symmetric w -cone distance in a TVS-CMS. Then, some types of various w -cone-contractions and the relations among them are investigated. Finally, as an application, a characterization of the completeness of TVS-cone metric regarding pre-symmetric concept is performed, which differentiates our results from former characterizations.

Suggested Citation

  • Seyedeh Sara Karimizad & Ghasem Soleimani Rad, 2024. "Pre-Symmetric w -Cone Distances and Characterization of TVS-Cone Metric Completeness," Mathematics, MDPI, vol. 12(12), pages 1-9, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:12:p:1833-:d:1413633
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    References listed on IDEAS

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    1. Salvador Romaguera & Pedro Tirado, 2024. "Presymmetric w -Distances on Metric Spaces," Mathematics, MDPI, vol. 12(2), pages 1-11, January.
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