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Issue ESAIM: Proc.
Volume 20, 2007
RFMAO 05 - Rencontres Franco-Marocaines en Approximation et Optimisation 2005
Page(s) 93 - 104
DOI http://dx.doi.org/10.1051/proc:072009
Published online 13 October 2007

ESAIM: Proc., 2007, Vol. 20, pp. 93-104
DOI: 10.1051/proc:072009

A construction of a maximal monotone extension of a monotone map

Jean-Pierre Crouzeix1, Eladio Ocaña Anaya2 and Wilfredo Sosa2

1  LIMOS, Université Blaise Pascal, 63170 Aubière, France.
2  Instituto de Matematica y Ciencias Afines, Jr Ancash 536, Cercado de Lima, Lima, Perú.


(Published online: 13 October 2007)

Abstract
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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