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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 176283, 14 pages
http://dx.doi.org/10.1155/2012/176283
Research Article

Existence and Iterative Algorithm of Solutions for a System of Generalized Nonlinear Mixed Variational-Like Inequalities

Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China

Received 29 December 2011; Accepted 16 January 2012

Academic Editor: Yonghong Yao

Copyright © 2012 Yan-Mei Du. 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 system of generalized nonlinear mixed variational-like inequality problems (SGNMVLIPs) in Banach spaces. The auxiliary principle technique is applied to study the existence and iterative algorithm of solutions for the SGNMVLIP. First, the existence of solutions of the auxiliary problems for the SGNMVLIP is shown. Second, an iterative algorithm for solving the SGNMVLIP is constructed by using this existence result. Finally, not only the existence of solutions of the SGNMVLIP is shown but also the convergence of iterative sequences generated by the algorithm is also proven. The technique and results presented in this paper generalize and unify the corresponding techniques and results given in the literature.