Minimax inequalities equivalent to the Fan-Knaster-Kuratowski-Mazurkiewicz theorems
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The purpose of this note is to give further generalizations of the Ky Fan minimax inequality by relaxing the compactness and convexity of sets and the quasi-concavity of the functional and to show that our minimax inequalities are equivalent to the Fan-Knaster-Kuratowski-Mazurkiewicz (FKKM) theorem and a modified FKKM theorem given in this note. 1993 Springer-Verlag New York Inc.