Fixed Point Theory and Applications
Volume 2007 (2007), Article ID 59262, 11 pages
Strong Convergence of Cesàro Mean Iterations for Nonexpansive Nonself-Mappings in Banach Spaces
Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
Received 9 March 2007; Accepted 12 September 2007
Academic Editor: Wataru Takahashi
Copyright © 2007 Rabian Wangkeeree. 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 uniformly convex Banach space which admits a weakly sequentially
continuous duality mapping from to , a nonempty closed convex subset of which is also a sunny nonexpansive retract of , and
a non-expansive nonself-mapping with . In this paper,
we study the strong convergence of two sequences generated by
for all , where , is a real sequence in an interval ,
and is a sunny non-expansive retraction of onto . We prove that
and converge strongly to and , respectively, as , where is
a sunny non-expansive retraction of onto . The results presented in this paper generalize, extend, and improve the corresponding results of Matsushita and Kuroiwa and many others.