Strong convergence of an iterative method for nonexpansive and accretive operators

Let X be a Banach space and A an m-accretive operator with a zero. Consider the iterative method that generates the sequence {xn} by the algorithm xn+1 = αnu+(1−αn)Jrnxn, where {αn} and {rn} are two sequences satisfying certain conditions, and Jr denotes the resolvent (I + rA)−1 for r >0. Strong convergence of the algorithm {xn} is proved assuming X either has a weakly continuous duality map or is uniformly smooth.  2005 Elsevier Inc. All rights reserved