On the Klee-Saint Raymond's characterization of convexity (Q2810552)
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scientific article; zbMATH DE number 6588583
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Klee-Saint Raymond's characterization of convexity |
scientific article; zbMATH DE number 6588583 |
Statements
3 June 2016
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convexity
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epi-pointed functions
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conjugate functions
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biconjugate functions
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locally convex spaces
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On the Klee-Saint Raymond's characterization of convexity (English)
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A new and more direct proof of a characterization of the convexity of functions in Banach spaces given in [\textit{J. Saint Raymond}, J. Nonlinear Convex Anal. 14, No. 2, 253--262 (2013; Zbl 1267.26012)], which generalizes an earlier statement in Hilbert spaces due to Klee, is provided in the more general setting of locally convex spaces and under weaker hypotheses, by means of convex analysis. Connections to other similar results from the literature are discussed, too.
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