Journal of Convex Analysis 18 (2011), No. 4, 1075--1091
Copyright Heldermann Verlag 2011
Generalized Monotone Operators, Generalized Convex Functions and Closed Countable Sets
László Szilárd
Faculty of Mathematics and Computer Sciences, Babes-Bolyai University, M. Kogalniceanu 1, 400084 Cluj-Napoca, Romania
laszlosziszi@yahoo.com
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.
Keywords: Generalized monotone map, generalized convex function, locally generalized monotone operator, closed countable set.
MSC: 03F15, 26A48, 26B25, 47H05
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