Minimax Inequalities for Vector-Valued Mappings on W-Spaces*

The topological KKM theorem of Chang et al. is slightly modified. By using our topological KKM theorem, we obtain a generalized section theorem and a generalized fixed point theorem on W-spaces which do not have any linear structure, and establish minimax inequalities for vector-valued mappings in Hausdorff topological vector spaces with closed pointed convex cones.