On Vector Implicit Variational Inequalities and Complementarity Problems

Abstract

In this paper, two vector implicit variational inequalities and three vector implicit complementarity problems are introduced with a more general order in ordered Banach spaces and the equivalence between them is studied under certain assumptions. Furthermore, some existence theorems of the vector implicit variational inequalities are proved. We answered the open question proposed by Rapcsak [Nonconvex Optim., Appl., Vol. 38, Kluwer Acad. Publ., Dordrecht, 2000, pp. 371---380].