A Hybrid Algorithm for Approximating a Common Element of Solutions of a Variational Inequality Problem and a Convex Feasibility Problem

Abstract

In this thesis, a hybrid 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 significant improvement of the results of Ceng et al. (J. Glob. Optim. 46(2010), 635-646). Finally, some applications of the theorem are presented.