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
收藏
页码：95 / 95
页数：1
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