A Note on Location of the Zeros of Quaternionic Polynomials

Abstract

The purpose of this paper is to investigate the extensions of the classical Eneström-Kakeya theorem and its various generalizations concerning the distribution of zeros of polynomials from the complex to the quaternionic setting. Using a maximum modulus theorem and the zero set structure in the recently published theory of regular functions and polynomials of a quaternionic variable, we construct new bounds of the Eneström-Kakeya type for the zeros of these polynomials. The obtained results for this subclass of polynomials and slice regular functions give generalizations of a number of results previously reported in the relevant literature.