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

Abstract EN

Let E be a real Banach space, and K a closed convex nonempty subset of E.

Let T1,T2,…,Tm:K→K be m total asymptotically nonexpansive mappings.

A simple iterative sequence {xn}n≥1 is constructed in E and necessary and sufficient conditions for this sequence to converge to a common fixed point of {Ti}i=1m are given.

Furthermore, in the case that E is a uniformly convex real Banach space, strong convergence of the sequence {xn}n=1∞ to a common fixed point of the family {Ti}i=1m is proved.

Our recursion formula is much simpler and much more applicable than those recently announced by several authors for the same problem.