Generalized vector -variational inequalities and vector -complementarity problems for point-to-set mappings

In this paper, we study a new generalized vector F -variational inequality and a new generalized vector F -complementarity problem for point-to-set mappings in Hausdorff topological vector spaces. We establish the equivalence between the generalized vector F -variational inequality and the generalized vector F -complementarity problem under certain assumptions. By considering the existence of solutions for the vector F -variational inequality with a single-valued mapping and using the continuous selection theorem, we obtain some new existence theorems of solutions for the generalized vector F -variational inequality and the generalized vector F -complementarity problem, respectively.