Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2012, Special Issue (2012), Article ID 194509, 38 pages.

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

Lu-Chuan Ceng and Ching-Feng Wen

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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.

Article information

Source
J. Appl. Math., Volume 2012, Special Issue (2012), Article ID 194509, 38 pages.

Dates
First available in Project Euclid: 3 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.jam/1357180315

Digital Object Identifier
doi:10.1155/2012/194509

Mathematical Reviews number (MathSciNet)
MR2861934

Zentralblatt MATH identifier
1242.49014

Citation

Ceng, Lu-Chuan; Wen, Ching-Feng. Well-Posedness by Perturbations of Generalized Mixed Variational Inequalities in Banach Spaces. J. Appl. Math. 2012, Special Issue (2012), Article ID 194509, 38 pages. doi:10.1155/2012/194509. https://projecteuclid.org/euclid.jam/1357180315


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