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Dualized and scaled Fitzpatrick functions
Author(s):
Stephen
Simons
Journal:
Proc. Amer. Math. Soc.
134
(2006),
2983-2987.
MSC (2000):
Primary 47H05;
Secondary 26B25
Posted:
May 4, 2006
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Abstract:
In this paper, we obtain an explicit formula for the interior of the domain of a maximal monotone multifunction in terms of its Fitzpatrick function.
References:
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- [1]
- J. M. Borwein, Maximal monotonicity via convex analysis, Preprint.
- [2]
- S. P. Fitzpatrick, Representing monotone operators by convex functions, Workshop/ Miniconference on Functional Analysis and Optimization, Proc. Centre Math. Anal. Austral. Nat. Univ., vol. 20, Austral. Nat. Univ., Canberra, 1988, pp. 59-65. MR 1009594 (90i:47054)
- [3]
- J.-J. Moreau, Fonctionelles convexes, Collège de France, Séminaire sur les équations aux derivées partielles, Paris, 1966.
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- R. T. Rockafellar, Level sets and continuity of conjugate convex functions, Trans. Amer. Math. Soc. 123 (1966), 46-63. MR 0192318 (33:544)
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- R. T. Rockafellar, Local boundedness of Nonlinear, Monotone Operators, Michigan Math. J. 16 (1969), 397-407.MR 0253014 (40:6229)
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- S. Simons, Minimax and monotonicity, Lecture Notes in Mathematics, vol. 1693, Springer-Verlag, 1998. MR 1723737 (2001h:49002)
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- S. Simons and C. Zalinescu, Fenchel duality, Fitzpatrick functions and maximal monotonicity, J. of Nonlinear and Convex Anal. 6 (2005), 1-22. MR 2138099
- [8]
- C. Zalinescu, Convex analysis in general vector spaces, World Scientific, 2002.MR 1921556 (2003k:49003)
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Additional Information:
Stephen
Simons
Affiliation:
Department of Mathematics, University of California, Santa Barbara, California 93106-3080
Email:
simons@math.ucsb.edu
DOI:
10.1090/S0002-9939-06-08363-8
PII:
S 0002-9939(06)08363-8
Keywords:
Monotone multifunction,
Fitzpatrick function,
convex function,
conjugate function,
Fenchel duality,
weak$^{*}$ topology
Received by editor(s):
May 3, 2005
Posted:
May 4, 2006
Communicated by:
Jonathan M. Borwein
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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