Geodesic
Generalized Monotone Operators, Generalized Convex Functions and Closed Countable Sets
Journal of convex analysis, Tome 18 (2011) no. 4, pp. 1075-1091.

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

We deal with operators which are monotone in several generalized sense. We show that if such property holds locally on the complement of a certain type of closed set, then the same property holds globally on the whole domain under some mild conditions. Our results extend similar statements already established for the classical Minty-Browder monotonicity. As applications we obtain some global generalized convexity results based on local generalized convexity property and some extra analytical requirements.
Classification : 03F15, 26A48, 26B25, 47H05
Mots-clés : Generalized monotone map, generalized convex function, locally generalized monotone operator, closed countable set 
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     author = {L. Szil\'ard},
     title = {Generalized {Monotone} {Operators,} {Generalized} {Convex} {Functions} and {Closed} {Countable} {Sets}},
     journal = {Journal of convex analysis},
     pages = {1075--1091},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {2011},
     url = {http://geodesic.mathdoc.fr/item/JCA_2011_18_4_JCA_2011_18_4_a9/}
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L. Szilárd. Generalized Monotone Operators, Generalized Convex Functions and Closed Countable Sets. Journal of convex analysis, Tome 18 (2011) no. 4, pp. 1075-1091. http://geodesic.mathdoc.fr/item/JCA_2011_18_4_JCA_2011_18_4_a9/