Inequalities and higher order convexity

Details Inequalities and higher order convexity Inequalities and higher order convexity

2011-08-26

arxiv.org/abs/1108.5249v1

Mathematics

Functional Analysis

Scientific paper

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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