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

• Main Authors: Lu-Chuan Ceng, Ching-Feng Wen
• Format: Article
• Language: English
• Published: Hindawi Limited 2012-01-01
• Series: Journal of Applied Mathematics
• Online Access: http://dx.doi.org/10.1155/2012/194509

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.