Inequalities and higher order convexity

Zarathustra Brady

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arXiv · 1108.5249

Inequalities and higher order convexity

Zarathustra Brady

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Abstract

We study the following problem: given n real arguments a1, ..., an and n real weights w1, ..., wn, under what conditions does the inequality w1 f(a1) + w2 f(a2) + ... + wn f(an) >= 0 hold for all functions f with nonnegative kth derivative for some given integer k? Using simple combinatorial techniques, we can prove many generalizations of theorems ranging from the Fuchs inequality to the criterion for Schur convexity.

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BibTeX RIS

Zarathustra Brady. 2011-08-26. Inequalities and higher order convexity. https://arxiv.org/abs/1108.5249

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