Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47H05

Retrieve articles in all journals with MSC (2000): 47H05


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
Email: benar@impa.br

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07083-7
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