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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, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:194509
    DOI: 10.1155/2012/194509
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    References listed on IDEAS

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    1. X. X. Huang, 2001. "Extended and strongly extended well-posedness of set-valued optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 53(1), pages 101-116, April.
    2. Eberhard Zeidler, 1985. "Nonlinear Functional Analysis and its Applications," Springer Books, Springer, number 978-1-4612-5020-3, March.
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