HYBRID STEEPEST-DESCENT METHOD WITH A COUNTABLY INFINITE FAMILY OF NONEXPANSIVE MAPPINGS ON BANACH SPACES

Abstract

In this paper, we propose an explicit iterative algorithm of hybrid steepest-descent type for finding a solution for variational inequalities over the set of common fixed points of an infinite family of nonexpansive mappings on real reflexive and strictly convex Banach spaces with a uniformly Gaˆteaux differentiable norm. A numerical example is also given for illustration.