Generalization of an Eneström-Kakeya type theorem to the quaternions
DOI:
https://doi.org/10.52737/18291163-2022.14.9-1-8Keywords:
Location of Zeros of a Polynomial, Eneström-Kakeya Theorem, Quaternionic PolynomialAbstract
The well-known Eneström-Kakeya theorem states that polynomial $p(z)=\sum_{\nu =0}^n a_\nu z^\nu$, where $0\leq a_0\leq a_1\leq \cdots\leq a_n$, has all of its (complex) zeros in $|z|\leq 1$. 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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