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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 928950, 12 pages
http://dx.doi.org/10.1155/2014/928950
Research Article

Convergence Theorems for Accretive Operators with Nonlinear Mappings in Banach Spaces

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

Received 4 December 2013; Accepted 17 March 2014; Published 29 April 2014

Academic Editor: Satit Saejung

Copyright © 2014 Yan-Lai Song and Lu-Chuan 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 strict pseudocontractions in infinite-dimensional Banach spaces. Under mild conditions, some weak and strong convergence theorems for approximating these common elements are proved. The methods in the paper are novel and different from those in the early and recent literature. Further, we consider the problem of finding a common element of the set of solutions of a mathematical model related to equilibrium problems and the set of fixed points of a strict pseudocontractions.