Abstract and Applied Analysis
Volume 2009 (2009), Article ID 573156, 17 pages
doi:10.1155/2009/573156
Research Article

Strong Convergence of Viscosity Iteration Methods for Nonexpansive Mappings

Jong Soo Jung

Department of Mathematics, Dong-A University, Busan 604-714, South Korea

Received 29 December 2008; Accepted 7 March 2009

Academic Editor: Simeon Reich

Copyright © 2009 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.

Abstract

We propose a new viscosity iterative scheme for finding fixed points of nonexpansive mappings in a reflexive Banach space having a uniformly Gâteaux differentiable norm and satisfying that every weakly compact convex subset of the space has the fixed point property for nonexpansive mappings. Certain different control conditions for viscosity iterative scheme are given and strong convergence of viscosity iterative scheme to a solution of a ceratin variational inequality is established.