Well-posedness by perturbations of generalized mixed variational inequalities in Banach spaces
Summary: 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 a 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.
generalized mixed variational inequalities
scientific article; zbMATH DE number 6021648
scientific article