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Techniques for maximal monotonicity Introduction

Summary: Techniques for maximal monotonicity
S. Simons
The purpose of this paper is to describe three techniques that are useful for the investigation
of monotone sets and multifunctions, and give two applications of them.
The three techniques use the "fg­theorem", the "big convexification" of a subset of
E × E
or a multifunction E 2E
(we suppose throughout that E is a nontrivial real
Banach space with dual E
), and the "convex function associated with a multifunction
E 2E
". The applications that we shall give will be the derivation of various criteria
for monotone subset of E × E
to be maximal monotone in the special case where E is
reflexive, and a slight generalization of Rockafellar's theorem on the maximal monotonicity
of the sum of maximal monotone multifunctions on a reflexive space. Remark 27 at the
end of the paper contains pointers to much stronger results that can be proved using these
We use a combination of the one­dimensional Hahn­Banach theorem, the Banach­


Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara


Collections: Mathematics