A minimax theorem for functions taking values in a Riesz space

The purpose of this paper is to prove minimax theorems for functions taking values in a Riesz space. In order to do this we first provide a suitable transposition to the Riesz space setting of a version of the Hahn Banach Theorem stated by Fuchssteiner and Konig. Although the two statement look similar, the proof in the Riesz space version is completely different; indeed the order given b the cone is not a well ordering, and therefore the proof of Fuchssteiner and Konig could not be adapted in this framework. Next we apply the Hahn-Banach version to derive some asymmetric minimax equalities.