Strong convergence of KrasnoselskiMann iteration for a countable family of asymptotically nonexpansive mappings in CAT(0) spaces

Based on a specific way of choosing the indices and a new concept, namely, an analogue of inner product, a modified KrasnoselskiMann iteration scheme is proposed for approximating common fixed points of a countable family of asymptotically nonexpansive mappings; and a strong convergence theorem is established in the framework of CAT(0) spaces. Our results greatly improve and extend those of the authors whose related researches just involve a single mapping and the weaker ∆convergence.