On the stability of iterative approximations to fixed points of nonexpansive mappings

We study iterative retraction approximations to fixed points of the nonexpansive self-mapping A:G→G given on the closed convex set G in a Banach space B. The conditions which guarantee weak and strong convergence and stability of these approximations with respect to perturbations of both operator A and constraint set G are considered. The results of this paper are new even in a Hilbert space for the iterative projection approximations. © 2006 Elsevier Inc. All rights reserved