Open Access

Viscosity approximation fixed points for nonexpansive and -accretive operators

Fixed Point Theory and Applications20062006:81325

DOI: 10.1155/FPTA/2006/81325

Received: 10 June 2006

Accepted: 22 July 2006

Published: 17 October 2006

Abstract

Let be a real reflexive Banach space, let be a closed convex subset of , and let be an -accretive operator with a zero. Consider the iterative method that generates the sequence by the algorithm where and are two sequences satisfying certain conditions, denotes the resolvent for , and let be a fixed contractive mapping. The strong convergence of the algorithm is proved assuming that has a weakly continuous duality map.

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Authors’ Affiliations

(1)
Department of Mathematics, Tianjin Polytechnic University

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Copyright

© R. Chen and Z. Zhu. 2006

This article is published under license to BioMed Central Ltd. 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.