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

 

On the convergence of maximal monotone operators


Authors: Jean-Paul Penot and Constantin Zalinescu
Journal: Proc. Amer. Math. Soc. 134 (2006), 1937-1946
MSC (2000): Primary 47H05; Secondary 26B25
Published electronically: December 16, 2005
MathSciNet review: 2215762
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Abstract: We study the convergence of maximal monotone operators with the help of representations by convex functions. In particular, we prove the convergence of a sequence of sums of maximal monotone operators under a general qualification condition of the Attouch-Brezis type.


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Additional Information

Jean-Paul Penot
Affiliation: Laboratoire de Mathématiques Appliquées, ERS CNRS 2055, Faculté des Sciences, av. de l’Université, 64000 Pau, France
Email: jean-paul.penot@univ-pau.fr

Constantin Zalinescu
Affiliation: Faculty of Mathematics, University “Al. I. Cuza” Iaşi, Bd. Carol I, Nr. 11, 700506 Iaşi, Romania
Email: zalinesc@uaic.ro

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08275-4
PII: S 0002-9939(05)08275-4
Keywords: Bounded convergence, convergence, convex function, maximal monotone operator, monotone operator, qualification condition
Received by editor(s): January 28, 2005
Received by editor(s) in revised form: February 1, 2005
Published electronically: December 16, 2005
Additional Notes: The second author was partially supported by Grant CEEX-05-D11-36.
Dedicated: Dedicated to F.E. Browder for the impact of his work on nonlinear analysis
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2005 American Mathematical Society