Approximating solutions of variational inequalities on the sets of common fixed points for a semigroup of asymptotically nonexpansive mappings in Banach spaces

Purpose: Our purpose in this paper is studying the strong convergence of implicit and explicit iterative schemes for approximating solutions of some variational inequalities on the sets of common fixed points for a semigroup of asymptotically nonexpansive mappings.Methods: We prove strong convergence theorems of such iterative scheme in a uniformly convex and uniformly smooth Banach spaces under certain conditions.Results: We obtain two convergence theorems of such iterative scheme for approximating a common fixed point, which is a unique solutions of the variational inequality.Conclusions: Our results extend and improve those of Zegeye et al., Sunthrayuth and Kumam, and Li et al. The methods of the proof given in this paper are also different.