Generalization of an Eneström-Kakeya type theorem to the quaternions - Gardner, Robert B.; Taylor, Mariah (Armenian Journal of Mathematics, 2022)
The well-known Eneström-Kakeya theorem states that polynomial $p(z)=\sum_{ u =0}^n a_ u z^ u$, where $0≤ a_0≤ a_1≤ …≤ a_n$, has all of its (complex) zeros in $|z|≤ 1$. 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.
Keywords: Location of Zeros of a Polynomial; Eneström-Kakeya Theorem; Quaternionic Polynomial