Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 284345, 12 pages
Approximation of Fixed Points of Nonexpansive Mappings and Solutions of Variational Inequalities
1The Abdus Salam International Centre for Theoretical Physics,
34014 Trieste, Italy
2Department of Mathematics and Statistics,
College of Sciences and Mathematics, Auburn University, Auburn, AL 36849, USA
3Department of Mathematical Sciences, Bayero University,
3011 Kano, Nigeria
Received 3 July 2007; Accepted 17 October 2007
Academic Editor: Siegfried Carl
Copyright © 2008 C. E. Chidume 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.
Let be a real -uniformly smooth Banach space with constant ,
. Let and be a nonexpansive map and an -strongly accretive map which is also -Lipschitzian, respectively. Let be a real sequence in that satisfies the following condition: and . For and , define a sequence iteratively in by , , . Then, converges strongly to the unique solution of the variational inequality problem (search for such that for all , where . A convergence theorem related to finite family of nonexpansive maps is also proved.