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PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
 

Summary: PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 00, Number 0, Xxxx XXXX, Pages 000--000
S 0002­9939(XX)0000­0 2000]Primary 47H05; Secondary 26B25
A NEW PROOF FOR ROCKAFELLAR'S CHARACTERIZATION
OF MAXIMAL MONOTONE OPERATORS
S. SIMONS AND C. Z –
ALINESCU
Abstract. We provide a new and short proof for Rockafellar's characteriza­
tion of maximal monotone operators in reflexive Banach spaces based on S.
Fitzpatrick's function and a technique used by R. S. Burachik and B. F. Svaiter
for proving their result on the representation of a maximal monotone operator
by convex functions.
1. The result
Throughout this note (X, #·#) is a reflexive Banach space and X # is its topological
dual space whose dual norm is denoted by #·# # . Then the topological dual of X×X #
is X # ×X, the pairing being given by #(x, x # ), (u # , u)# := #x, u # #+#u, x # # , where, as
usual, #x, u # # := u # (x) for x # X and u # # X # . Let A : X ¶ X # be a multivalued
operator (or multifunction) whose graph gr A := {(x, x # ) | x # # A(x)} is nonempty.
Recall that A is monotone if

  

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

 

Collections: Mathematics