On generalized pointwise noncyclic contractions without proximal normal structure

Abstract

In this article, we introduce a new class of noncyclic mappings called generalized pointwise noncyclic contractions, and we prove a best proximity pair theorem for this class of noncyclic mappings in the setting of strictly convex Banach spaces. Our conclusions generalize a result due to Kirk and Royalty. We also study convergence of iterates of noncyclic contraction mappings in uniformly convex Banach spaces.