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arXiv · 1612.08191

On a minimax theorem: an improvement, a new proof and an overview of its applications

Biagio Ricceri
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Abstract

Theorem 1 of [14], a minimax result for functions $f:X\times Y\to {\bf R}$, where $Y$ is a real interval, was partially extended to the case where $Y$ is a convex set in a Hausdorff topological vector space ([15], Theorem 3.2). In doing that, a key tool was a partial extension of the same result to the case where $Y$ is a convex set in ${\bf R}^n$ ([7], Theorem 4.2). In the present paper, we first obtain a full extension of the result in [14] by means of a new proof fully based on the use of the result itself via an inductive argument. Then, we present an overview of the various and numerous applications of these results.

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Biagio Ricceri. 2016-12-24. On a minimax theorem: an improvement, a new proof and an overview of its applications. https://arxiv.org/abs/1612.08191

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