Abstract: The existence and connectedness of solutions for weak vector variational inequalities and their scalarization with a C-monotone mapping from a topological vector space to continuous linear mapping space L(X, Y) are shown. With the C-weak hemicontinuity and C-monotonicity for a mapping, and setvalued mapping fixed point theorems, the connectedness are derived by discussing the properties of set-valued mapping induced by solution sets of a scalarization variational inequality related to the weak vector variational inequalities.

Key words: Weak vector variational inequalities, Scalarization vector variational inequalities, Dual cone, C-weak hemicontinuous, C-Monotone.