| Issue |
ESAIM: Proc.
Volume 20, 2007
RFMAO 05 - Rencontres Franco-Marocaines en Approximation et Optimisation 2005
|
|
|---|---|---|
| Page(s) | 93 - 104 | |
| DOI | https://doi.org/10.1051/proc:072009 | |
| Published online | 13 October 2007 | |
A construction of a maximal monotone extension of a monotone map
1
LIMOS, Université Blaise Pascal, 63170 Aubière, France.
2
Instituto de Matematica y Ciencias Afines, Jr Ancash 536, Cercado de Lima, Lima, Perú.
A proof based on the axiom of choice shows that any monotone map has maximal monotone extensions but this proof is not constructive. In this paper, we give a construction of such an extension. The process is based on some density properties of (maximal) monotone maps given before.
Résumé
Afin de montrer qu'une multi-application monotone possède une extension maximale monotone, on utilise en général l'axiome du choix ou, ce qui est équivalent, le lemme de Zorn. Ce procédé est alors non constructif. Nous proposons ici une démonstration constructive de cette extension.
Mathematics Subject Classification: 47H05 / 47H04
Key words: Multivalued maps / Monotonicity / Maximal Monotonocity.
© EDP Sciences, ESAIM, 2007
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