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

Lu-Chuan Ceng and Ching-Feng Wen

Journal of Applied Mathematics, 2012, vol. 2012, 1-38

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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:194509

DOI: 10.1155/2012/194509

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