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PreprintarXiv licencearXiv

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 Gmathringarding's cones and k-convex cones.

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Cite

BibTeXRIS
BibTeX
@misc{cao2026newtontype,
  title = {{New Newton-type inequality and a unified perspective on Maclaurin's inequality via the inclusion relations of cones}},
  author = {Ning Cao and Xuanxuan Hu and Feida Jiang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.28544},
  eprint = {2610.28544},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.28544},
}
RIS
TY  - UNPB
TI  - New Newton-type inequality and a unified perspective on Maclaurin's inequality via the inclusion relations of cones
AU  - Ning Cao
AU  - Xuanxuan Hu
AU  - Feida Jiang
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.28544
UR  - https://arxiv.org/abs/2610.28544
AB  - 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 Gmathringarding's cones and k-convex cones.
ER  -