A two-function minimax theorem

摘要

1. Introduction. Let X, Y be two non-empty sets and f, g two real functions on Xx I In this paper, we consider the problem of guaranteeing the validity of the inequality. In the sequel, it is implicitly assumed that sup inf g(x,y)< + oo. Several papers have already been devoted to this problem. Most of them are quoted in a very recent survey by S. Simons [2] to which we also refer for a discussion of the above inequality. A feature which is common to each of that papers is to assume the condition.