Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 635382, 24 pages
doi:10.1155/2010/635382
Research Article

A Hybrid Proximal Point Three-Step Algorithm for Nonlinear Set-Valued Quasi-Variational Inclusions System Involving (A,η)-Accretive Mappings

Hong-Gang Li,1 An Jian Xu,1 and Mao Ming Jin2

1Institute of Applied Mathematics Research, Chongqing University of Posts and TeleCommunications, Chongqing 400065, China
2Institute of Nonlinear Analysis Research, Changjiang Normal University, Chongqing, Fuling 400803, China

Received 29 December 2009; Accepted 7 April 2010

Academic Editor: Nanjing Jing Huang

Copyright © 2010 Hong-Gang Li et al. 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 main purpose of this paper is to introduce and study a new class of generalized nonlinear set-valued quasi-variational inclusions system involving (A,η)-accretive mappings in Banach spaces. By using the resolvent operator due to Lan-Cho-Verma associated with (A,η)-accretive mappings and the matrix analysis method, we prove the convergence of a new hybrid proximal point three-step iterative algorithm for this system of set-valued variational inclusions and an existence theorem of solutions for this kind of the variational inclusions system. The results presented in this paper generalize, improve, and unify some recent results in this field.