Journal of Applied Mathematics (Jan 2012)

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

  • Lu-Chuan Ceng,
  • Ching-Feng Wen

DOI
https://doi.org/10.1155/2012/194509
Journal volume & issue
Vol. 2012

Abstract

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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.