Inequalities for convex functions
A. W. J. Stoddart (1967)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Inequalities for convex functions
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Characterization of convex functions
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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.