We deal with the minimax problem relative to a vector-valued function f: X0xY0--> V, where a partial ordering in the topological vector space V is induced by a closed and convex cone C. In Ref. 1, under suitable hypotheses, we proved that [GRAPHICS] the exact meaning of the symbols is given in Section 2. In this work, we prove that, under a reasonable setting of hypotheses, the previous inclusion holds and also we have that [GRAPHICS]