A new version of the Hahn-Banach theorem
type: Item
instance of: scholarly article
title: A new version of the Hahn-Banach theorem
zbMATH Open document ID: 1040.46004
published in: Archiv der Mathematik
publication date: 2003-11-17T00:00:00Z
review text: An abstract general version of the Hahn-Banach theorem is shown, in the spirit of earlier works of H. König and the same author. This result is then applied to many natural situations from convex analysis, such as Moreau-Fenchel duality between convex functions and Rockafellar's surjectivity theorem for maximal monotone multifunctions in reflexive Banach spaces. It is also shown that a maximal monotone multifunction on a normed space with bounded range has full domain. An interesting feature of this approach is that it allows to bypass on several occasions the use of Brouwer's fixed point theorem.
Mathematics Subject Classification ID: 46A22
Mathematics Subject Classification ID: 46N10
Mathematics Subject Classification ID: 49J35
Mathematics Subject Classification ID: 47H05
zbMATH DE Number: 2004963
zbMATH Keywords: convex analysis
zbMATH Keywords: monotone multifunctions
author: Stephen Simons
reviewed by: Gilles Godefroy
MaRDI profile type: Publication
full work available at URL: s00013-003-0500-2
OpenAlex ID: W1991932889
DOI: 10.1007/S00013-003-0500-2
description: scientific article; zbMATH DE number 2004963