Journal of Applied Mathematics
Volume 2012 (2012), Article ID 264721, 22 pages
http://dx.doi.org/10.1155/2012/264721
Research Article

Metric Characterizations of -Well-Posedness for a System of Mixed Quasivariational-Like Inequalities in Banach Spaces

L. C. Ceng1,2 and Y. C. Lin3

1Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
2Scientific Computing Key Laboratory of Shanghai Universities, Shanghai 200234, China
3Department of Occupational Safety and Health, College of Public Health, China Medical University, Taichung 404, Taiwan

Received 2 October 2011; Accepted 9 October 2011

Academic Editor: Yonghong Yao

Copyright © 2012 L. C. Ceng and Y. C. Lin. 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 investigate the problems of the well-posedness for a system of mixed quasivariational-like inequalities in Banach spaces. First, we generalize the concept of -well-posedness to the system of mixed quasivariational-like inequalities, which includes symmetric quasi-equilibrium problems as a special case. Second, we establish some metric characterizations of -well-posedness for the system of mixed quasivariational-like inequalities. Under some suitable conditions, we prove that the -well-posedness is equivalent to the existence and uniqueness of solution for the system of mixed quasivariational-like inequalities. The corresponding concept of -well-posedness in the generalized sense is also considered for the system of mixed quasivariational-like inequalities having more than one solution. The results presented in this paper generalize and improve some known results in the literature.