[Banach] Abstract of a paper by Hichem Ben-El-Mechaiekh

This is an announcement for the paper "Intersection Theorems for Closed Convex Sets and Applications" by Hichem Ben-El-Mechaiekh.

Abstract: A number of landmark existence theorems of nonlinear functional analysis follow in a simple and direct way from the basic separation of convex closed sets in finite dimension via elementary versions of the Knaster-Kuratowski-Mazurkiewicz principle - which we extend to arbitrary topological vector spaces - and a coincidence property for so-called von Neumann relations. The method avoids the use of deeper results of topological essence such as the Brouwer fixed point theorem or the Sperner's lemma and underlines the crucial role played by convexity. It turns out that the convex KKM principle is equivalent to the Hahn-Banach theorem, the Markov-Kakutani fixed point theorem, and the Sion-von Neumann minimax principle.

Archive classification: math.FA

Mathematics Subject Classification: Primary: 52A07, 32F32, 32F27, Secondary: 47H04, 47H10, 47N10

Submitted from: hmechaie@brocku.ca

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1501.05813

or

http://arXiv.org/abs/1501.05813