A general two-function minimax theorem

A two-function minimax theorem is proved. In this result, the concavity-convexity conditions of both functions involve monotone transforms and mixing of functional values, and the “wupwardness/w-downwardness” conditions; both spaces are required to be compact topological spaces but without linear structure. By this result, an open question proposed by Forgó and Joó in 1998 is answered.