Semi-normal structure and best proximity pair results in convex metric spaces

Abstract

A new geometric notion on a nonempty and convex pair of subsets of a convex metric space $X$, called semi-normal structure, is introduced and used to investigate the existence of best proximity pairs for a new class of mappings, called strongly noncyclic relatively C-nonexpansive. We also study the structure of minimal sets of strongly noncyclic relatively C-nonexpansive mappings in the setting of convex metric spaces.