Armenian Journal of Mathematics, 14(9)
2022; 1–8
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Generalization of an Eneström-Kakeya type theorem to the quaternions

Robert Gardner*, Mariah Taylor

Received: 2024-12-05 · Published: 2022-06-29

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CC BY 4.0 This work is licensed under a Creative Commons Attribution 4.0 International License.
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Original title
Generalization of an Eneström-Kakeya type theorem to the quaternions
Authors
Robert Gardner, Mariah Taylor
Source journal
Armenian Journal of Mathematics, 14(9)
Published
2022-06-29
Licence
Creative Commons Attribution 4.0 International
Original
https://doi.org/10.52737/18291163-2022.14.9-1-8

Abstract

The well-known Eneström-Kakeya theorem states that polynomial p(z)=∑nν=0aνzνp(z)=∑ν=0naνzν, where 0≤a0≤a1≤⋯≤an0≤a0≤a1≤⋯≤an, has all of its (complex) zeros in |z|≤1|z|≤1. Many generalizations of this result exist in the literature. In this paper, we extend one such result to the quaternionic setting and state one of the possible corollaries.
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