Approximation of common fixed points of an infinite family of nonexpansive mappings in Banach spaces

Let C be a closed convex subset of a real uniformly smooth and strictly convex Banach space E. Consider the following iterative algorithm given by where f is a contraction on C and Wn is a mapping generated by an infinite family of nonexpansive mappings . Assume that the set of common fixed points of this infinite family of nonexpansive mappings is not empty. In this paper, we prove that the sequence {xn} generated by the above iterative algorithm converges strongly to a common fixed point of , which solves some variational inequality. Our results improve and extend the results announced by many others.