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.
Citation
Lu-Chuan Ceng. Ching-Feng Wen. "Well-Posedness by Perturbations of Generalized Mixed Variational Inequalities in Banach Spaces." J. Appl. Math. 2012 (SI03) 1 - 38, 2012. https://doi.org/10.1155/2012/194509
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