Zeros of One Class of Quaternionic Polynomials

Abstract

The goal of this paper is to study the properties of zeros of some special quaternionic polynomials with restricted coefficients, namely coefficients whose real and imaginary components satisfy suitable inequalities. We extend the well-known Enestr\"{o}m-Kakeya theorem and its various generalizations from complex to the quaternionic setting. The main tools used to derive the bounds for the zeros of these polynomials are the maximum modulus theorem and the structure of the zero sets established in the newly developed theory of regular functions and polynomials of a quaternionic variable.