On the zero bounds of polynomials and regular functions of a quaternionic variable

Abstract

In this manuscript, we are concerned with the problem of locating the zeros of some special quaternionic polynomials and regular functions with restricted coefficients; namely quaternionic coefficients whose real components or their moduli satisfy suitable inequalities. The obtained results for this subclass of quaternionic polynomials and regular functions produce extensions of the classical Enestr?m-Kakeya theorem and its various variants from complex to the quaternionic setting.