International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 615107, 17 pages
doi:10.1155/2009/615107
Research Article

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

C. E. Chidume1 and E. U. Ofoedu2

1The Abdus Salam International Centre for Theoretical Physics, 34151 Trieste, Italy
2Department of Mathematics, Nnamdi Azikiwe University, P.M.B. 5025, Awka, Anambra State, Nigeria

Received 10 July 2009; Accepted 26 October 2009

Academic Editor: Gelu Popescu

Copyright © 2009 C. E. Chidume and E. U. Ofoedu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.