The Eneström–Kakeya Theorem for polynomials of a quaternionic variable

Generalization of an Eneström-Kakeya type theorem to the quaternions

“…. , n. If Corollary 1 is related to Theorem 9 of [2]; the outer radius of these two results are the same but Corollary 1 also gives an inner radius of the zero containing region.…”

“…The Eneström-Kakeya theorem has recently been extended to polynomials of a quaternionic variable as follows [2].…”

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

“…In the same paper, Carney et al [3] also established the following generalization of Theorem 7 to quaternionic coefficients in the form of the following result.…”

“…This number system of quaternions is denoted by H in honor of Hamilton. This theory of quaternions is by now very well developed in many different directions, and we refer the reader to [19] for the basic features of quaternionic functions (see also recent papers [3], [13], [14]).…”

“…Very recently, Carney et al [3] extended the Eneström-Kakeya theorem and its various generalizations from complex polynomials to quaternionic polynomials by making use of Theorems 5 and 6. Firstly, they established the following quaternionic analogue of Theorem 1.…”