… A new brief proof of Fan's minimax theorem for convex-concave like functions is established
… concave like on X × Y. Suppose that X is compact and f(., y) is lower semicontinuous on X for …

… Neumann's theorem. H. Nikaidό [7], on the other hand, using Brouwer's fixed point theorem,
… hyperplane and yields the theorem of Kneser-Fan (see 4.2), and the other uses a fixed point …

… of Theorem 2 to a function on a product set A χ F immediately yields the principal minimax
theorem of the note, Theorem 3, … of Fan's and Sion's general minimax theorems. These …

… for infinite games (for instance, the generalized Ville's minimax theorem as stated in our … of
part (ii) of Theorem 1). Since the proof of (ii) is based on von Neumann's minimax theorem, its …

… FAN Theorem 3 includes Ville's minimax theorem, which we state in a much more general
form: Let X1, X2 be two compact spaces and let so be a realvalued continuous function on X1 …

… relationship between Theorem A and the topological minimax theorems given in [7]. In
Section 1 we point out that Theorem A is a consequence of a vector space minimax theorem due …

… minimax theorem sacrifices, on the contrary, the algebraic conditions to a certain degree for
the benefit of the weaker topological condition* on … that neither Fan's convexity concept [2] …

… ON FAN’S MINIMAX INEQUALITY … Using this fixed point theorem, we now prove the first
version of Fan’s minimax inequality. THEOREM 2.3. Let C be a nonempty compact conex subset …

… Ky Fan Cl J. In the second part (as an application) we give a further generalization of the Ky
Fan-Nikaido-Kneser Theorem … results is based on the von Neumann Minimax Theorem in Rn …

… use in proving both our minimax theorem for the saddle case (Theorem 1 in §3) … on their
extension of Fan's lemma, with which they also treat several applications apart from minimax …