Some elementary general principles of convex analysis
The aim of the paper is to provide simple proofs of several results, stated in super-reflexive Banach spaces, concerning minimization of quasi-convex functions, variational inequalities, game theory, systems of inequalities, and maximal monotone operators, by using the following ``intersection principle'': Let \((E,|\cdot|)\) be super-reflexive and let \(\{C_i\mid i\in I\}\) be a family of closed convex sets in \(E\) with the finite intersection property. If \(C_{i_0}\) is bounded for some \(i_0\in I\), then the intersection \(\bigcap\{C_i\mid i\in I\}\) is not empty. As the authors point out, most of the results are valid for arbitrary reflexive spaces.
scientific article; zbMATH DE number 807912