On zero inclusion regions of polynomials and regular functions of a quaternionic variable

Abstract

One of the most fundamental problems in numerical mathematics is the estimation of the zeros of a polynomial. This kind of study for polynomials and regular functions of a quaternionic variable has been carried out by many authors in the recent past. In this paper, we build a framework that uses the zero sets of a regular product and the extended Schwarz's lemma to deduce zero inclusion regions of polynomials and regular functions with quaternionic coefficients located on only one side of the powers of the quaternionic variable. The results obtained for this particular subclass of regular functions lead to the generalisation of other results that are known in the relevant literature.