$W$-convexity on the Isbell-convex hull of an asymmetrically normed real vector space

Abstract

In their previous work, K\"unzi and Yilzid introduced the concept of convexity structures in the sense of Takahashi in quasi-pseudometric spaces. In this article, we continue the study of this theory for instance we introduce the concept of $W$-convexity for real-valued pair of functions defined on an asymmetrically normed real vector space. Moreover, we show that all minimal pair of functions defined on an asymmetrically normed real vector space equipped with a convex structure $W$ which is $W$-convex whenever $W$ is translation-invariant.