A new iteration method for common fixed points of an infinite family of nonself asymptotically nonexpansive mappings

Abstract

In this paper, we mainly study the convergence theorem for common fixed points of an infinte family of nonself asymptotically nonexpansive mappings form a nonempty closed convex subset of a real uniformly convex Banach space to the whole space. By using a specific way of choosing the indexes of the involved mappings, we propose an optimum iterative approach to approximating common fixed points of countable families. Under some suitable conditons, a strong convergence theorem of the mappings is obtained. The result extends the situation of finite families of such mappings.