Generalized Vector Complementarity Problems With Corresponding Vector Variational Inequality Problems

In this paper, We introduce a new class of generalized vector complementarity problems and the corresponding generalized vector variational inequality problems which include many known complementarity problems and the corresponding vector variational inequality problems as special cases and establish the equivalence between those problems in Banach spaces. Furthermore, we obtain some new existence theorems of solutions to the generalized vector complementarity problems and the generalized vector variational inequality problems under some suitable assumption swithout any monotonicity.