Strong convergence of an iterative method for nonexpansive and accretive operators

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:314

Article

Xu, HK

关键词: iterative method;    nonexpansive mapping;    m-accretive operator;    weakly continuous duality map;    uniformly smooth Banach space;   

DOI  :  10.1016/j.jmaa.2005.04.082

来源: Elsevier

【 摘 要 】

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

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