Some elementary general principles of convex analysis
type: Item
instance of: scholarly article
title: Some elementary general principles of convex analysis
zbMATH Open document ID: 0877.49006
DOI: 10.12775/TMNA.1995.002
published in: Topological Methods in Nonlinear Analysis
publication date: 1997-12-08T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 49J27
Mathematics Subject Classification ID: 47H05
Mathematics Subject Classification ID: 46N10
Mathematics Subject Classification ID: 47J20
Mathematics Subject Classification ID: 49J40
zbMATH DE Number: 807912
zbMATH Keywords: KKM-maps
zbMATH Keywords: intersection principle
zbMATH Keywords: super-reflexive Banach spaces
zbMATH Keywords: minimization of quasi-convex functions
zbMATH Keywords: variational inequalities
zbMATH Keywords: game theory
zbMATH Keywords: systems of inequalities
zbMATH Keywords: maximal monotone operators
author: Andrzej Granas
author: Marc Lassonde
reviewed by: Constantin Zălinescu
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 807912