Convex Sets in Proximal Relator Spaces

Abstract

This article introduces convex sets in finite-dimensional normed linear spaces equipped with a proximal relator.    A proximal relator is a nonvoid family of proximity relations $\mathcal{R}_{\delta}$ (called a proximal relator) on a nonempty set.  A normed linear space endowed with $\mathcal{R}_{\delta}$ is an extension of the Sz\'{a}z relator space.  This leads to a basis for the study of the nearness of convex sets in proximal linear spaces.