Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 167535, 14 pages
Convergence on Composite Iterative Schemes for Nonexpansive Mappings in Banach Spaces
Department of Mathematics, Dong-A University, Busan 604-714, South Korea
Received 13 January 2008; Revised 5 April 2008; Accepted 3 May 2008
Academic Editor: Mohammed Khamsi
Copyright © 2008 Jong Soo Jung. 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 reflexive Banach space with a uniformly Gâteaux differentiable norm. Suppose that every weakly compact convex subset of has the fixed point property for nonexpansive mappings. Let be a nonempty closed convex
subset of , a contractive mapping (or a weakly contractive mapping),
and nonexpansive mapping with the fixed point set . Let be generated by a new composite iterative scheme: , , . It is proved that converges strongly to
a point in , which is a solution of certain variational inequality provided that
the sequence satisfies and , for some and the sequence is asymptotically regular.