Maximal monotonicity, conjugation and the duality product
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- by Regina Sandra Burachik and B. F. Svaiter PDF
- Proc. Amer. Math. Soc. 131 (2003), 2379-2383 Request permission
Abstract:
Recently, the authors studied the connection between each maximal monotone operator $T$ and a family $\mathcal {H}(T)$ of convex functions. Each member of this family characterizes the operator and satisfies two particular inequalities. The aim of this paper is to establish the converse of the latter fact. Namely, that every convex function satisfying those two particular inequalities is associated to a unique maximal monotone operator.References
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Additional Information
- Regina Sandra Burachik
- Affiliation: Engenharia de Sistemas e Computação, COPPE–UFRJ CP 68511, Rio de Janeiro–RJ, CEP 21945–970 Brazil
- Email: regi@cos.ufrj.br
- B. F. Svaiter
- Affiliation: IMPA Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro–RJ, CEP 22460-320 Brazil
- MR Author ID: 304617
- Email: benar@impa.br
- Received by editor(s): February 28, 2002
- Published electronically: March 18, 2003
- Additional Notes: The first author was partially supported by CNPq and by PRONEX–Optimization
The second author was partially supported by CNPq Grant 301200/93-9(RN) and by PRONEX–Optimization. - Communicated by: Jonathan M. Borwein
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 2379-2383
- MSC (2000): Primary 47H05
- DOI: https://doi.org/10.1090/S0002-9939-03-07053-9
- MathSciNet review: 1974634