Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 168468, 12 pages
Iterative Schemes for Zero Points of Maximal Monotone Operators and Fixed Points of Nonexpansive Mappings and Their Applications
1School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, China
2Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, South Korea
Received 16 August 2007; Accepted 25 November 2007
Academic Editor: Massimo Furi
Copyright © 2008 Li Wei and Yeol Je Cho. 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.
Two iterative schemes for finding a common element of the set of zero
points of maximal monotone operators and the set of fixed points of nonexpansive mappings in the
sense of Lyapunov functional in a real uniformly smooth and uniformly convex Banach space are
obtained. Two strong convergence theorems are obtained which extend some previous work.
Moreover, the applications of the iterative schemes are demonstrated.