Generalization of an Eneström-Kakeya type theorem to the quaternions

Author(s)

Generalization of an Eneström-Kakeya type theorem to the quaternions Robert Gardner

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.

DOI: 10.52737/18291163-2022.14.9-1-8 Armenian Journal of Mathematics, 14(9) 1-8

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Keywords

Location of Zeros of a Polynomial, Eneström-Kakeya Theorem, Quaternionic Polynomial

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