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.
Let be a real Banach space, and a closed convex nonempty subset of .
Let be total asymptotically nonexpansive mappings. A
simple iterative sequence is constructed in and necessary and sufficient
conditions for this sequence to converge to a common fixed point of are given. Furthermore, in the case that 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.