Inequalities and higher order convexity
Functional Analysis
2011-08-29 v1
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.
Cite
@article{arxiv.1108.5249,
title = {Inequalities and higher order convexity},
author = {Zarathustra Brady},
journal= {arXiv preprint arXiv:1108.5249},
year = {2011}
}