On w-Isbell-convexity

Olivier Olela Otafudu; Katlego Sebogodi

doi:10.4995/agt.2022.15739

Authors

Olivier Olela Otafudu North-West University https://orcid.org/0000-0001-9593-7899
Katlego Sebogodi University of Johannesburg

DOI:

https://doi.org/10.4995/agt.2022.15739

Keywords:

Modular pseudometric, Isbell-convexity, $w$-Isbell-convexity

Abstract

Chistyakov introduced and developed a concept of modular metric for an arbitrary set in order to generalise the classical notion of modular on a linear space. In this article, we introduce the theory of hyperconvexity in the setting of modular pseudometric that is herein called w-Isbell-convexity. We show that on a modular set, w-Isbell-convexity is equivalent to hyperconvexity whenever the modular pseudometric is continuous from the right on the set of positive numbers.

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Author Biographies

Olivier Olela Otafudu, North-West University

School of Mathematical and Statistical Sciences

Katlego Sebogodi, University of Johannesburg

Department of Mathematics and Applied Mathematics

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