On the Enestrom-Kakeya theorem for quaternionic polynomial

Abstract

The problem of determining the zeros of regular polynomials of a quaternionic variable with quaternionic coefficients is addressed in this study. The main aim of this paper is to study the extensions of the classical Enestrom-Kakeya theorem and its various generalizations about the distribution of zeros of polynomials from complex to the quaternionic setting. We shall also derive zero free regions of some special regular functions of a quaternionic variable with restricted coefficients, namely quaternionic coefficients or real parts or their moduli satisfy suitable inequalities. The obtained results for this subclass of polynomials and slice regular functions produce generalizations of a number of results known in the literature on this subject.