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

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  • Lu-Chuan Ceng
  • Ching-Feng Wen

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.

Suggested Citation

  • Lu-Chuan Ceng & Ching-Feng Wen, 2012. "Well-Posedness by Perturbations of Generalized Mixed Variational Inequalities in Banach Spaces," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-38, December.
    • Handle: RePEc:hin:jnljam:194509
    DOI: 10.1155/2012/194509
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