Strong convergence of Krasnoselski-Mann iteration for a countable family of asymptotically nonexpansive mappings in CAT(0) spaces
Shanguang Qian, Wei-Qi Deng · The Journal of Nonlinear Sciences and Applications · 2017
Based on a specific way of choosing the indices and a new concept, namely, an analogue of inner product, a modified Krasnoselski-Mann 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 \(\Delta\)-convergence.