Intersection theorems for closed convex sets and applications
type: Item
instance of: scholarly article
title: Intersection theorems for closed convex sets and applications
zbMATH Open document ID: 1341.52002
author: Hichem Ben-El-Mechaiekh
published in: Missouri Journal of Mathematical Sciences
publication date: 2016-03-15T00:00:00Z
full work available at URL: https://arxiv.org/abs/1501.05813
full work available at URL: https://projecteuclid.org/euclid.mjms/1449161367
review text: By using a standard separation theorem, the author proves first the convex KKM theorem (the Ky Fan KKM principle, when the involved mapping is convex-valued). Then, this result provides simple proofs of several fundamental results from the KKM theory: fixed point or coincidence theorems, variational inequalities, minimax inequalities, etc. The used method avoids deeper arguments of topological essence such as the Brouwer fixed point theorem or the Sperner's lemma and underlines the crucial role played by convexity.
reviewed by: Mircea Balaj
Mathematics Subject Classification ID: 52A07
Mathematics Subject Classification ID: 32F32
Mathematics Subject Classification ID: 32F27
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47N10
zbMATH DE Number: 6555650
zbMATH Keywords: separation of convex sets
zbMATH Keywords: intersection theorems
zbMATH Keywords: convex KKM theorem
zbMATH Keywords: fixed points for von Neumann relations
zbMATH Keywords: coincidence
zbMATH Keywords: systems of nonlinear inequalities
zbMATH Keywords: variational inequalities
zbMATH Keywords: minimization of functionals
zbMATH Keywords: Markov-Kakutani fixed point theorem
zbMATH Keywords: Hahn-Banach theorem
MaRDI profile type: Publication
arXiv ID: 1501.05813
description: scientific article; zbMATH DE number 6555650