A Note on Location of the Zeros of Quaternionic Polynomials

Author(s)

A Note on Location of the Zeros of Quaternionic Polynomials Irfan Ahmad Wani

The purpose of this paper is to investigate the extensions of the classical Eneström-Kakeya theorem and its various generalizations concerning the distribution of zeros of polynomials from the complex to the quaternionic setting. Using a maximum modulus theorem and the zero set structure in the recently published theory of regular functions and polynomials of a quaternionic variable, we construct new bounds of the Eneström-Kakeya type for the zeros of these polynomials. The obtained results for this subclass of polynomials and slice regular functions give generalizations of a number of results previously reported in the relevant literature.

DOI: 10.52737/18291163-2023.15.7-1-12 Armenian Journal of Mathematics, 15(7) 1-12

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Keywords

Quaternionic Polynomial, Zeros, Eneström-Kakeya theorem

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