Nonsmooth vector variational inequalities on Hadamard manifold and their existence

In this paper, we consider nonsmooth vector variational inequality problems (NVVIP), Minty nonsmooth vector variational inequality problems (MNVVIP) and d-Perturbed nonsmooth vector variation inequality problems (d-PNVVIP) on Hadamard manifold using the concept of bifunctions. We define the class of R-+(p)- pseudomonotonicity, v-continuity and geodesic upper sign continuity of vector valued bifunctions on Hadamard manifold and establish relations among them. Furthermore, some existence results for NVVIP, MNVVIP and d-PNVVIP are derived. These results extend some known corresponding results in the literature.