Saved in:
Bibliographic Details
Main Author: Ren, Changyu
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2501.07613
Tags: Add Tag
No Tags, Be the first to tag this record!
Table of Contents:
  • 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 $\al_1,\al_2,\cdots,\al_s$ satisfy the condition that the polynomial $$t^s+\al_1 t^{s-1}+\al_2 t^{s-2}+\cdots+\al_s $$ has only real roots, the Newton-Maclaurin type inequalities hold for $S_{k;s}(x)$.