A New Iteration Process for Approximation of Common Fixed Points for Finite Families of Total Asymptotically Nonexpansive Mappings

Abstract

Let E be a real Banach space, and K a closed convex nonempty subset of E . Let T 1 , T 2 , …, T m : K → K be m total asymptotically nonexpansive mappings. A simple iterative sequence is constructed in E and necessary and sufficient conditions for this sequence to converge to a common fixed point of are given. Furthermore, in the case that E is a uniformly convex real Banach space, strong convergence of the sequence to a common fixed point of the family is proved. Our recursion formula is much simpler and much more applicable than those recently announced by several authors for the same problem.