Fixed Point Theory and Applications
Volume 2006 (2006), Article ID 81325, 10 pages
doi:10.1155/FPTA/2006/81325
Viscosity approximation fixed points for nonexpansive and
m-accretive operators
Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China
Received 10 June 2006; Accepted 22 July 2006
Copyright © 2006 Rudong Chen and Zhichuan Zhu. 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
Let X
be a real reflexive Banach space, let C
be a closed convex subset of X, and let A be an m-accretive operator with a zero. Consider the iterative method that generates the sequence {xn} by the algorithm
xn+1=αnf(xn)+(1−αn)Jrnxn, where αn and γn are two sequences satisfying certain
conditions, Jr denotes the resolvent (I+rA)−1 for r>0, and let
f:C→C be a fixed contractive mapping. The strong
convergence of the algorithm {xn} is proved assuming that X
has a weakly continuous duality map.