A general form of Newton-Maclaurin type inequalities

2025/01/13 by Changyu Ren, Ren, Changyu
Mathematics · #Functional Equations Stability Results #Mathematical Inequalities and Applications #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2501.07613

Abstract

In this paper, we extend the classical Newton-Maclaurin inequalities to functions S_k;s(x)=E_k(x)+\dsum_i=1^s \al_i E_k-i(x), which are formed by linear combinations of multiple basic symmetric mean. We proved that when the coefficients \al₁,\al₂,⋯,\al_s satisfy the condition that the polynomial t^s+\al₁ t^s-1+\al₂ t^s-2+⋯+\al_s has only real roots, the Newton-Maclaurin type inequalities hold for S_k;s(x).

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