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Abstract and Applied Analysis
Volume 2014, Article ID 659870, 11 pages
http://dx.doi.org/10.1155/2014/659870
Research Article

Stable Perturbed Iterative Algorithms for Solving New General Systems of Nonlinear Generalized Variational Inclusion in Banach Spaces

1Department of Mathematics, Sichuan University of Science and Engineering, Zigong, Sichuan 643000, China
2Key Laboratory Higher Education of Sichuan Province for Enterprise Informationalization and Internet of Things, Zigong, Sichuan 643000, China

Received 19 June 2014; Accepted 26 July 2014; Published 14 October 2014

Academic Editor: Jong Kyu Kim

Copyright © 2014 Ting-jian Xiong and Heng-you Lan. 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

We introduce and study a new general system of nonlinear variational inclusions involving generalized -accretive mappings in Banach space. By using the resolvent operator technique associated with generalized -accretive mappings due to Huang and Fang, we prove the existence theorem of the solution for this variational inclusion system in uniformly smooth Banach space, and discuss convergence and stability of a class of new perturbed iterative algorithms for solving the inclusion system in Banach spaces. Our results presented in this paper may be viewed as an refinement and improvement of the previously known results.