• Corpus ID: 119172895

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

@article{Ricceri2016OnAM,
  title={On a minimax theorem: an improvement, a new proof and an overview of its applications},
  author={Biagio Ricceri},
  journal={arXiv: Functional Analysis},
  year={2016}
}

• B. Ricceri
• Published 24 December 2016
• Mathematics
• arXiv: Functional Analysis

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.