Weak convergence theorem of asymptotically nonexpansive mappings in Banach space
Gang Li · Journal of Yangzhou University · 2004
Let X be a uniformly convex Banach space such that X* has the Kadec-Klee property. Let C be a closed convex subset of X, G be a directed system and {Tt,t∈G} be asymptotically nonexpansive mappings on C. It is proved in this paper that, if x0∈C satisfies (a) lim sups∈G lim supt∈G ‖ T5Ttx0-Ttx0 ‖=0, (b) lim sups∈G lim supt∈G ‖TsTtx0-TtTsx0 ‖=0, then there exists a p∈AF((?)), such that Txx0(?)p.