Approximating fixed points of α-nonexpansive mappings in uniformly convex Banach spaces and CAT(0) spaces

Abstract

An existence theorem for a fixed point of an α-nonexpansive mapping of a nonempty bounded, closed and convex subset of a uniformly convex Banach space has been recently established by Aoyama and Kohsaka with a non-constructive argument. In this paper, we show that appropriate Ishikawa iterate algorithms ensure weak and strong convergence to a fixed point of such a mapping. Our theorems are also extended to CAT(0) spaces. AMS Subject Classification: 54E40, 54H25, 47H10, 37C25. © 2013 Naraghirad et al.; licensee Springer.