Generalized vector F-variational inequalities and vector F-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. (C) 2008 Elsevier Ltd. All rights reserved.