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arXiv · 2610.28544

New Newton-type inequality and a unified perspective on Maclaurin's inequality via the inclusion relations of cones

Ning Cao·Xuanxuan Hu·Feida Jiang
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Abstract

The classical Newton-Maclaurin's inequalities for the elementary symmetric means are well known. In this paper, we derive a new class of Newton-type inequalities and generalize Maclaurin's inequality by connecting the elementary symmetric functions with their counterparts. Our idea is mainly motivated by the inclusion relations of G$\mathring{\text{a}}$rding's cones and $k$-convex cones.

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Ning Cao, Xuanxuan Hu, Feida Jiang. 2026-10-20. New Newton-type inequality and a unified perspective on Maclaurin's inequality via the inclusion relations of cones. https://arxiv.org/abs/2610.28544

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