Some inequalities for convex functions or order n

J. D. Kečkić

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Some inequalities for convex functions or order n

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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.