A Krasnoselskii-Type Algorithm for Approximating Solutions of Variational Inequality Problems and Convex Feasibility Problems

Abstract

A Krasnoselskii-type algorithm for approximating a common element of the set of solutions of a variational inequality problem for a monotone, k-Lipschitz map and solutions of a convex feasibility problem involving a countable family of relatively nonexpansive maps is studied in a uniformly smooth and 2-uniformly convex real Banach space. A strong convergence theorem is proved. Some applications of the theorem are presented.