STABILITY OF THE ITERATION METHOD FOR NON EXPANSIVE MAPPINGS
Bernard Lemaire · 1996
Abstract. The general iteration method for nonexpansive mappings on a Banach space is considered. Under some assumption of fast enough convergence on the sequence of (“almost ” nonexpansive) perturbed iteration mappings, if the basic method is τ−convergent for a suitable topology τ weaker than the norm topology, then the perturbed method is also τ−convergent. Application is presented to the gradient-prox method for monotone inclusions in Hilbert spaces. 1. Introduction. Let