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Proceedings of the American Mathematical Society

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Geometric Newton inequalities


Author: James M. Ni
Journal: Proc. Amer. Math. Soc. 149 (2021), 2609-2623
MSC (2020): Primary 53A15, 52A39, 52B60
DOI: https://doi.org/10.1090/proc/15372
Published electronically: March 25, 2021
MathSciNet review: 4246811
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Abstract: In this article, we take a geometric approach to extend Newton’s well-known inequalities. A family of inequalities, which are invariant under affine transformations, is proposed for parallelotopes. We prove some of them and show the connections they have with matrix inequalities, convex geometry, and geometric inequalities.


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Additional Information

James M. Ni
Affiliation: Westview High School, 13500 Camino Del Sur, San Diego, California 92129
ORCID: 0000-0002-6646-3564
Email: liamgotelgoog@gmail.com

Received by editor(s): August 3, 2020
Received by editor(s) in revised form: August 10, 2020, and September 2, 2020
Published electronically: March 25, 2021
Communicated by: Jia-Ping Wang
Article copyright: © Copyright 2021 American Mathematical Society