SOME SADDLE-POINT THEOREMS FOR VECTOR-VALUED MULTIMAPPING

Abstract

In this paper, we prove the existence of a saddle point for a multivalued mapping that takes
values in a general vector space with the condition that (v,C)-cyclic quasi-monotonicity in the
direction. The problem is setting in an environment that does not have any topological structure
and use assumptions about the convexity of the multivalued mapping and the convexity of the cone
that make the order in the range of objective mapping.