A hybrid algorithm for approximating solutions of a variational inequality problem and a convex feasibility problem

Abstract

In this paper, an extragradient-like iteration algorithm for approximating a common element of the set of solutions of a variational inequality problem for a monotone, k-Lipschitz map and common fixed points of a countable family of relatively nonexpansive maps in a uniformly smooth and 2-uniformly convex real Banach space is introduced. A strong convergence theorem for the sequence generated by this algorithm is proved. The theorem obtained is a an improvement of some recent important results. Finally, some applications of the theorem are presented.