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Maximal monotonicity via convex analysis

Borwein, Jonathan M. (2006) Maximal monotonicity via convex analysis. Journal of Convex Analysis, 13 (3-4). pp. 561-586.

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    Abstract

    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. Many other extension, surjectivity, convexity and local boundedness results are likewise established.

    Item Type: Article
    Uncontrolled Keywords: monotone operators, convex analysis, sandwich theorem, Fenchel duality, sum theorem, composition theorem, extension theorems, cyclic monotonicity, acyclic monotonicity, Fitzpatrick function
    Subjects: UNSPECIFIED
    Faculty: UNSPECIFIED
    Depositing User: Dr David Allingham
    Date Deposited: 28 Sep 2012 12:05
    Last Modified: 12 Jan 2015 13:06
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1235

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