ON A GENERALIZATION OF A NORMAL MAP AND EQUATION

The class of normal maps was recently investigated by Robinson and Ral ph in connection with the study of a variational inequality defined on a polyhedral set. In this paper a generalization of such a map is con sidered, and the associated generalized normal equation is studied. Th e latter provides a unified formulation of several generalized variati onal inequality and complementarity problems. Using degree theory, som e sufficient conditions for the existence of a zero of a generalized n ormal map are established and the stability of a generalized normal eq uation at a solution is analyzed. Specializations of the results to va rious applications are discussed.