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.
"On generalized pointwise noncyclic contractions without proximal normal structure." Ann. Funct. Anal. 9 (2) 220 - 232, May 2018. https://doi.org/10.1215/20088752-2017-0049