A generalization of Bernstein-Doetsch Theorem
Abstract: Let V be an open convex subset of a nontrivial real normed space X. In the paper we give a partial generalization of Bernstein-Doetsch Theorem. We prove that if there exist a base ℬ of X and a point x ∈ V such that a midconvex function f: X → ℝ is locally bounded above on b-ray at x for each b ∈ ℬ, then f is convex. Moreover, we show that under the above assumption, f is also continuous in case X = ℝN, but not in general.
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Bibliographic citation
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A generalization of Bernstein-Doetsch Theorem ; volume:45 ; number:1 ; year:2012 ; pages:35-38 ; extent:4
Demonstratio mathematica ; 45, Heft 1 (2012), 35-38 (gesamt 4)
- Creator
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Mureńko, Anna
- DOI
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10.1515/dema-2013-0362
- URN
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urn:nbn:de:101:1-2411171657288.169426126476
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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15.08.2025, 7:21 AM CEST
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Associated
- Mureńko, Anna
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