Geodesic
Extended Sums and Extended Compositions of Monotone Operators
Journal of convex analysis, Tome 13 (2006) no. 3, pp. 721-738

Voir la notice de l'article provenant de la source Heldermann Verlag

We study extended notions for sums of monotone operators and for precompositions of monotone operators with continuous linear mappings. First, we establish some new properties related to the notion of extended sum recently proposed by Revalski and Théra, among them the monotonicity of this sum provided the operators involved are maximal monotone. Then, we show that the equivalence which exists between usual sums and compositions remains valid also for the extended operations. This allows us to obtain some known and new results for extended compositions via the corresponding properties of extended sums.
Classification : 47H05, 52A41, 26B25
Mots-clés : Monotone operators, extended sums of monotone operators, compositions, enlargements, subdifferentials 
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     title = {Extended {Sums} and {Extended} {Compositions} of {Monotone} {Operators}},
     journal = {Journal of convex analysis},
     pages = {721--738},
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     url = {http://geodesic.mathdoc.fr/item/JCA_2006_13_3_JCA_2006_13_3_a14/}
}
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Y. García; M. Lassonde; J. P. Revalski. Extended Sums and Extended Compositions of Monotone Operators. Journal of convex analysis, Tome 13 (2006) no. 3, pp. 721-738. http://geodesic.mathdoc.fr/item/JCA_2006_13_3_JCA_2006_13_3_a14/