Fixed point solutions of variational inequalities for a finite family of asymptotically nonexpansive mappings in banach spaces¹

Let E be a real Banach space with a uniformly Gâteaux differentiable norm possessing uniform normal structure, C a nonempty closed bounded convex subset of E. By using viscosity approximation methods for a finite family of asymptotically non-expansive mappings, sufficient and necessary conditions for the iterative sequence to converging to the common fixed point are obtained. The results presented in the paper improve and generalize known results in the literature.