Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 168468, 12 pages
Research Article

Iterative Schemes for Zero Points of Maximal Monotone Operators and Fixed Points of Nonexpansive Mappings and Their Applications

Li Wei1 and Yeol Je Cho2

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.