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Journal of Applied Mathematics
Volume 2012, Article ID 194509, 38 pages
http://dx.doi.org/10.1155/2012/194509
Research Article

Well-Posedness by Perturbations of Generalized Mixed Variational Inequalities in Banach Spaces

1Department of Mathematics, Scientific Computing Key Laboratory of Shanghai Universities, Shanghai Normal University, Shanghai 200234, China
2Center for General Education, Kaohsiung Medical University, Kaohsiung 80708, Taiwan

Received 24 September 2011; Accepted 3 November 2011

Academic Editor: Yeong-Cheng Liou

Copyright © 2012 Lu-Chuan Ceng and Ching-Feng Wen. 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 consider an extension of the notion of well-posedness by perturbations, introduced by Zolezzi (1995, 1996) for a minimization problem, to a class of generalized mixed variational inequalities in Banach spaces, which includes as a special case the class of mixed variational inequalities. We establish some metric characterizations of the well-posedness by perturbations. On the other hand, it is also proven that, under suitable conditions, the well-posedness by perturbations of a generalized mixed variational inequality is equivalent to the well-posedness by perturbations of the corresponding inclusion problem and corresponding fixed point problem. Furthermore, we derive some conditions under which the well-posedness by perturbations of a generalized mixed variational inequality is equivalent to the existence and uniqueness of its solution.