Characterization of convex functions
Jacek Tabor ; Józef Tabor
Studia Mathematica, Tome 192 (2009), p. 29-37 / Harvested from The Polish Digital Mathematics Library
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There are many inequalities which in the class of continuous functions are equivalent to convexity (for example the Jensen inequality and the Hermite-Hadamard inequalities). We show that this is not a coincidence: every nontrivial linear inequality which is valid for all convex functions is valid only for convex functions.

Publié le : 2009-01-01
EUDML-ID : urn:eudml:doc:285040 
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Jacek Tabor; Józef Tabor. Characterization of convex functions. Studia Mathematica, Tome 192 (2009) pp. 29-37. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm192-1-3/