NEWTON-LIKE INEQUALITIES FOR LINEAR COMBINATIONS

被引：0

作者：

Bautista-Ramos, Cesar

Guillen-Galvan, Carlos

Gomez-Salgado, Paulino

机构：

来源：

MATHEMATICAL INEQUALITIES & APPLICATIONS | 2025年 / 28卷 / 01期

关键词：

Newton's inequalities; Newton-like inequalities; log-concave sequence; ele mentary symmetric polynomials; normalized elementary symmetric polynomials; CONCAVE;

D O I：

10.7153/mia-2025-28-06

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We provide conditions under which linear combinations of normalized elementary symmetric polynomials satisfy some Newton-like inequalities. Namely, the log-concavity of the coefficients and nonnegativity of the arguments. We prove that such conditions are essential. That is, dropping any of these conditions leads to counterexamples. This settled a conjecture of Ren [C. Ren, A generalization of Newton-Maclaurin's inequalities, Int. Math. Res. Not. IMRN 5, (2024), 3799-3822].

引用

页码：95 / 95

页数：1

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