Du-subsets of ordered Banach spaces and their best approximation properties with applications

Abstract

The main goal of this paper is to investigate the best approximation of sets that do not correspond to proximal sets. We call these new sets “Du-sets”. “D” and “u” refer to the relationship that these sets can have with downward and upward. The closed Du-sets are not necessarily convex, upward, downward, or star-shaped, but are nevertheless proximal. We will also achieve some useful and practical results.