Quaternionic Generalization of the Eneström-Kakeya Theorem

Abstract

{In 2020, Carney et.al. proved the quaternionic version of the Eneström-Kakeya Theorem, which states that a polynomial $p(q)={\sum }_{\hat{I}½=0}^n{q}^{\hat{I}}½a_{\hat{I}}½$ with non-negative and monotonically increasing coefficients $(0<a_0\le a_1\le \cdots \le a_n)$ has all of its zeros within the unit ball $|q|\le 1$. Numerous generalizations of Eneström-Kakeya Theorem are available in the literatures (\cite{m}-\cite{mmr}). In this paper, we extend some of these generalizations to the quaternionic context and present several potential results.}

10 pages