关于一个极小极大定理的改进、新证明及其应用
On a minimax theorem: an improvement, a new proof and an overview of its applications
摘要：
[14]的定理1是函数$f:X\times Y\to {\bf R}$的极小极大结果，其中$Y$是实区间，该定理被部分地推广到$Y$是Hausdorff拓扑向量空间中的凸集的情况（[15]，定理3.2）。在这样做时，一个关键工具是将相同结果部分扩展到$Y$是${\bf R}^n$中的凸集的情况（[7]，定理4.2）。在本文中，我们首先通过一个新的证明，得到了[14]中结果的一个完全推广，这个新的证明完全基于通过一个归纳论证使用结果本身。然后，我们提出了这些结果的各种和众多的应用的概述。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
