Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 22, No 3, (1996), 331p-340p
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.