Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

László Szilárd

Faculty of Mathematics and Computer Sciences, Babeş-Bolyai University, M. Kogălniceanu 1, 400084 Cluj-Napoca, Romania

laszlosziszi@yahoo.com

Keywords

  • Generalized monotone map
  • generalized convex function
  • locally generalized monotone operator
  • closed countable set

Mathematics Subject Classification

03F15, 26A48, 26B25, 47H05

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Suggested citation

L. Szilárd. “Generalized Monotone Operators, Generalized Convex Functions and Closed Countable Sets.” Journal of Convex Analysis 18 (2011), No. 4, 1075–1091. https://doi.org/10.68381/jca18066

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Published by Heldermann Verlag, 2011. Rights now held by Banach Press LLC.