Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 168468, 12 pages
doi:10.1155/2008/168468
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
Abstract
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.