IMPLICIT PREDICTOR-CORRECTOR ITERATION PROCESS FOR FINITELY MANY ASYMPTOTICALLY (QUASI-)NONEXPANSIVE MAPPINGS

We study an implicit predictor-corrector iteration process for finitely many asymptoti-cally quasi-nonexpansive self-mappings on a nonempty closed convex subset of a Banach space E. We derive a necessary and sufficient condition for the strong convergence of this iteration process to a common fixed point of these mappings. In the case E is a uniformly convex Banach space and the mappings are asymptotically nonexpansive, we verify the weak (resp., strong) convergence of this iteration process to a common fixed point of these mappings if Opial’s condition is satisfied (resp., one of these mappings is semicom-pact). Our results improve and extend earlier and recent ones in the literature. Copyright © 2006 L. C. Ceng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. Introduction an