Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

Next Article

Journal of Convex Analysis 13 (2006), No. 3, 561--586
Copyright Heldermann Verlag 2006

Maximal Monotonicity via Convex Analysis

Jonathan Borwein
Faculty of Computer Science, Dalhousie University, Halifax, N.S., Canada B3H 1W5

In his "23 Mathematische Probleme" lecture to the Paris International Congress in 1900, David Hilbert wrote "Besides it is an error to believe that rigor in the proof is the enemy of simplicity."
In this spirit, we use simple convex analytic methods, relying on an ingenious function due to Simon Fitzpatrick, to provide a concise proof of the maximality of the sum of two maximal monotone operators on reflexive Banach space under standard transversality conditions. Various other surjectivity, convexity and local boundedness results are likewise established.

Keywords: Monotone operators, convex analysis, sandwich theorem, Fenchel duality, sum theorem.

[ Fulltext-pdf  (1216  KB)] for subscribers only.