Some new results on cyclic relatively nonexpansive mappings in convex metric spaces

In this article, we prove a best proximity point theorem for generalized cyclic contractions in convex metric spaces. Then we investigate the structure of minimal sets of cyclic relatively nonexpansive mappings in the setting of convex metric spaces. In this way, we obtain an extension of the Goebel-Karlovitz lemma, which is a key lemma in fixed point theory.