Fixed Point Theory and Applications
Volume 2007 (2007), Article ID 064874, 10 pages
A New Iterative Algorithm for Approximating Common Fixed Points for Asymptotically Nonexpansive Mappings
1Department of Applied Mathematics, North China Electric Power University, Baoding 071003, China
2Department of Mathematics Education and RINS, College of Natural Sciences, Gyeongsang National University, Chinju 660-701, South Korea
Received 28 February 2007; Accepted 13 April 2007
Academic Editor: Nan-Jing Huang
Copyright © 2007 H. Y. Zhou et al. 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.
Suppose that is a nonempty closed convex subset of a real uniformly convex and smooth Banach space with as a sunny nonexpansive retraction. Let be two weakly inward and asymptotically nonexpansive mappings with respect to with sequences , , respectively. Suppose that is a sequence in generated iteratively by , , for all , where , , and are three real sequences in for some which satisfy condition . Then, we have the following. (1) If one of and is completely continuous or demicompact and , then the strong convergence of to some is established. (2) If is a real uniformly convex Banach space satisfying Opial's condition or whose norm is Fréchet differentiable, then the weak convergence of to some is proved.