A fixed point theorem for pointwise eventually nonexpansive mappings in nearly uniformly convex Banach spaces

The purpose of this paper is to prove the existence of a fixed point for a pointwise eventually nonexpansive mapping in a nearly uniformly convex Banach space. This provides an affirmative answer to a question given by Kirk and Xu [W.A. Kirk, Hong-Kun Xu, Asymptotic pointwise contraction, Nonlinear Anal. 69 (2008), 4706–4712].