Equivalence of a Ky Fan type minimax theorem and a Gordan type alternative theorem (Q1117445)

An equivalence between minimax theorems of Ky Fan type and alternative theorems of Gordan type with weakened convexlike hypothesis is proved. The proofs of Ky Fan type minimax theorems often required a fixed point theorem or the Von Neumann minimax theorem, whereas the proofs of Gordan type theorems usually require a separation theorem. The equivalence provides an alternative way of proving both these types of theorems, and shows that if one of these theorems has been proved then the other can easily by verified from it.