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