Weak Convergence of a Projection Algorithm for Variational Inequalities and Relatively Nonexpansive Mappings in a Banach Space

Abstract:

      In this paper, we introduce an iterative sequence for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping in a Banach space. Then we show that the sequence converges weakly to a common element of two sets.