A STEEPEST-DESCENT KRASNOSEL’SKII–MANN ALGORITHM FOR AN INFINITE FAMILY OF NONEXPANSIVE MAPPINGS

Abstract

For solving a variational inequality problem over the common fixed point set of an infinite family of nonexpansive mappings on uniformly smooth Banach spaces or reflexive and strictly convex ones with a uniformly Gâteaux differentiable norm, we consider an explicit iteration method, based on the steepest-descent and Krasnosel’skii–Mann algorithms. We also show that some modifications of the last are special case of our result.