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A new proof for Rockafellar's characterization of maximal monotone operators
Author(s):
S.
Simons;
C.
Zalinescu
Journal:
Proc. Amer. Math. Soc.
132
(2004),
2969-2972.
MSC (2000):
Primary 47H05;
Secondary 26B25
Posted:
June 2, 2004
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Abstract:
We provide a new and short proof for Rockafellar's characterization 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.
References:
-
- 1.
- R. S. Burachik and B. F. Svaiter, Maximal monotonicity, conjugation and the duality product, Proc. Amer. Math. Soc. 131 (2003), 2379-2383. MR 2004a:49037
- 2.
- S. Fitzpatrick, Representing monotone operators by convex functions, Workshop/Miniconference on Functional Analysis and Optimization (Canberra, 1988), Austral. Nat. Univ., Canberra, 1988, pp. 59-65.
- 3.
- J.-P. Gossez, Opérateurs monotones non linéaires dans les espaces de Banach non réflexifs J. Math. Anal. Appl. 34 (1971), 371-395. MR 47:2442
- 4.
- J. E. Martinez-Legaz and M. Théra, A convex representation of maximal monotone operators, J. Nonlinear Convex Anal. 2 (2001), 243-247. MR 2002e:49035
- 5.
- J.-P. Penot, The relevance of convex analysis for the study of monotonicity, Tech. report, University of Pau, Pau, 2002.
- 6.
- R. T. Rockafellar, On the maximality of sums of nonlinear monotone operators, Trans. Amer. Math. Soc. 149 (1970), 75-88. MR 43:7984
- 7.
- S. Simons, Minimax and monotonicity, Springer-Verlag, Berlin, 1998. MR 2001h:49002
- 8.
- S. Simons, Maximal monotone multifunctions of Brøndsted-Rockafellar type, Set-Valued Anal. 7 (1999), 255-294. MR 2001b:47100
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Additional Information:
S.
Simons
Affiliation:
Department of Mathematics, University of California, Santa Barbara, California 93106
Email:
simons@math.ucsb.edu
C.
Zalinescu
Affiliation:
Faculty of Mathematics, University ``Al. I. Cuza'' Iasi, Bd. Carol I, Nr. 11, 700506 Iasi, Romania
Email:
zalinesc@uaic.ro
DOI:
10.1090/S0002-9939-04-07462-3
PII:
S 0002-9939(04)07462-3
Keywords:
Maximal monotone operator,
convex function,
duality mapping
Received by editor(s):
February 6, 2003
Posted:
June 2, 2004
Communicated by:
Jonathan M. Borwein
Copyright of article:
Copyright
2004,
American Mathematical Society
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