Geodesic
Generalized Monotone Operators, Generalized Convex Functions and Closed Countable Sets
Journal of convex analysis, Tome 18 (2011) no. 4, pp. 1075-1091 Cet article a éte moissonné depuis la source Heldermann Verlag

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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 
@article{JCA_2011_18_4_JCA_2011_18_4_a9,
     author = {L. Szil\'ard},
     title = {Generalized {Monotone} {Operators,} {Generalized} {Convex} {Functions} and {Closed} {Countable} {Sets}},
     journal = {Journal of convex analysis},
     pages = {1075--1091},
     year = {2011},
     volume = {18},
     number = {4},
     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/