Journal of Applied Mathematics
Volume 2011 (2011), Article ID 961038, 26 pages
http://dx.doi.org/10.1155/2011/961038
Research Article

A New System of Generalized Mixed Quasivariational Inclusions with Relaxed Cocoercive Operators and Applications

Zhongping Wan,1 Jia-Wei Chen,1,2 Hai Sun,2 and Liuyang Yuan1

1School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, China
2School of Mathematics and Information, China West Normal University, Nanchong, Sichuan 637002, China

Received 21 April 2011; Accepted 12 June 2011

Academic Editor: Yongkun Li

Copyright © 2011 Zhongping Wan 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

A new system of generalized mixed quasivariational inclusions (for short, SGMQVI) with relaxed cocoercive operators, which develop some preexisting variational inequalities, is introduced and investigated in Banach spaces. Next, the existence and uniqueness of solutions to the problem (SGMQVI) are established in real Banach spaces. From fixed point perspective, we propose some new iterative algorithms for solving the system of generalized mixed quasivariational inclusion problem (SGMQVI). Moreover, strong convergence theorems of these iterative sequences generated by the corresponding algorithms are proved under suitable conditions. As an application, the strong convergence theorem for a class of bilevel variational inequalities is derived in Hilbert space. The main results in this paper develop, improve, and unify some well-known results in the literature.