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

Seyedeh Sara Karimizad and Ghasem Soleimani Rad ()
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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

Mathematics, 2024, vol. 12, issue 12, 1-9

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.

Keywords: pre-symmetric w-cone distance; TVS-CMS; Suzuki-type contraction; Minkowski functional; completeness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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