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Journal of Applied Mathematics
Volume 2014, Article ID 943753, 11 pages
http://dx.doi.org/10.1155/2014/943753
Research Article

Weak and Strong Convergence Theorems for Zeroes of Accretive Operators in Banach Spaces

1Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
2Department of Mathematics, Shanghai Normal University, Scientific Computing Key Laboratory of Shanghai University, Shanghai 200234, China

Received 22 October 2013; Accepted 28 January 2014; Published 13 March 2014

Academic Editor: Alberto Cabada

Copyright © 2014 Yanlai Song and Luchuan Ceng. 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

The purpose of this paper is to present two new forward-backward splitting schemes with relaxations and errors for finding a common element of the set of solutions to the variational inclusion problem with two accretive operators and the set of fixed points of nonexpansive mappings in infinite-dimensional Banach spaces. Under mild conditions, some weak and strong convergence theorems for approximating this common elements are proved. The methods in the paper are novel and different from those in the early and recent literature. Our results can be viewed as the improvement, supplementation, development, and extension of the corresponding results in the very recent literature.