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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Fixed points in the family of convex representations of a maximal monotone operator

Author: B. F. Svaiter
Journal: Proc. Amer. Math. Soc. 131 (2003), 3851-3859
MSC (2000): Primary 47H05
Published electronically: May 5, 2003
MathSciNet review: 1999934
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Abstract: Any maximal monotone operator can be characterized by a convex function. The family of such convex functions is invariant under a transformation connected with the Fenchel-Legendre conjugation. We prove that there exists a convex representation of the operator which is a fixed point of this conjugation.

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Additional Information

B. F. Svaiter
Affiliation: IMPA Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro–RJ, CEP 22460-320 Brazil

PII: S 0002-9939(03)07083-7
Keywords: Maximal monotone operators, conjugation, convex functions
Received by editor(s): July 31, 2002
Published electronically: May 5, 2003
Additional Notes: This work was partially supported by CNPq Grant 301200/93-9(RN) and by PRONEX–Optimization
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2003 American Mathematical Society

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