Strong convergence of implicit and explicit iterations for a class of variational inequalities in Banach spaces

In this paper, we introduce and analyze implicit and explicit iteration methods for solving a variational inequality problem over the set of common fixed points of an infinite family of nonexpansive mappings on a real reflexive and strictly convex Banach space with a uniformly Gateaux differentiable norm. Strong convergence results are given. Our results improve and extend the corresponding results in the literature.