A Nontopological Two-function Minimax Theorem with Monotone Transformations of the Functional Values
A two-function minimax inequality with the following characteristics is proved: (i) the function on the less-side of the inequality is generalized concave in its first variable while the function on the greater-side is generalized convex in its second variable, (ii) generalized convexity/concavity is defined in terms of averages of monotone transformations of values of both functions, (iii) the proof is elementary, neither separation nor fixed-point theorems are used.
KeywordsVariational Inequality Generalize Convex Noncooperative Game Minimax Theorem Monotone Transformation
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