2011/08/26 by Zarathustra Brady, Brady, Zarathustra
Computer Science · Mathematics · #26A51 #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Mathematical Inequalities and Applications #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.1108.5249
openalex publication_date 2011/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.