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

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.