Approximation of common fixed points for finite families of total asymptotically nonexpansive mappings

Let E be a real Banach space, K a closed convex nonempty subset of E. Let T1,T2, . . . , Tm :K →K be m total asymptotically nonexpansive mappings. An iterative sequence for approximation of common fixed points (assuming existence) of T1,T2, . . . , Tm is constructed; necessary and sufficient conditions for the convergence of the scheme to a common fixed point of the mappings are given. Furthermore, in the case that E is uniformly convex, a sufficient condition for convergence of the iteration process to a common fixed point of mappings under our setting is established. © 2006 Elsevier Inc. All rights reserved.