Exceptional family of elements for generalized variational inequalities
Xiaolan Liu · Journal of Inequalities and Applications · 2013
This paper introduces the notion of exceptional family of elements for generalized variational inequalities in Hilbert spaces. The set-valued mapping is assumed to be upper semi-continuous compact with nonempty closed convex values. Based on topological degree for set-valued mappings, instead of the technique of continuous selection, an alternative theorem is obtained which says that the generalized variational inequalities have either a solution or an exceptional family of elements. In addition, an existing result of a solution for generalized variational inequalities is obtained. MSC: 90C25, 90C33.