A general nontopological two-function minimax theorem (Q1293307)

The authors present a more general version of a minimax theorem given by \textit{B.-L. Lin} and \textit{X.-C. Quan} [Arch. Math. 57, 75-79 (1991; Zbl 0696.49032)]. The inequality \[ \inf_{x\in X}\sup_{y\in Y}f(x, y)\leq \sup_{x\in X}\inf_{y\in Y} f(x,y) \] is shown under the assumptions that \(f: X\times Y\to \mathbb{R}\) is convex-like and bounded, that \(g: X\times Y\to \mathbb{R}\) is concave-like, and that always \(f(x,y)\leq g(x,y)\).