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, issue 1

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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https://doi.org/10.1155/2012/194509

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2012:y:2012:i:1:n:194509

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