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Dualized and scaled Fitzpatrick functions
Author:
Stephen Simons
Journal:
Proc. Amer. Math. Soc. 134 (2006), 2983-2987
MSC (2000):
Primary 47H05; Secondary 26B25
Posted:
May 4, 2006
MathSciNet review:
2231623
Full-text PDF Free Access
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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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J. M. Borwein, Maximal monotonicity via convex analysis, Preprint.
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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
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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:
http://dx.doi.org/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
Article copyright:
© Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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