Generalized vector variational inequalities over countable product of sets

In this paper, we consider vector variational inequalities with set-valued mappings over countable product sets in a real Banach space setting. By employing concepts of relative pseudomonotonicity, we establish several existence results for ge-ne-ra-lized vector variational inequalities and for systems of genera-li-zed vector variational inequalities. These results strengthen previous existence results which were based on the usual monotonicity type assumptions.