Korean J. Math. Vol. 30 No. 3 (2022) pp.503-512
DOI: https://doi.org/10.11568/kjm.2022.30.3.503

A note on Enstrom-Kakeya theorem for quaternionic polynomials

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Published: Sep 30, 2022
Keywords:
Quaternionic Polynomial, Zeros, Enestrom-Kakeya theorem.
Mathematics Subject Classification:
30E10, 30G35, 16K20.

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Adil Hussain Malik
Department of Mathematics, University of Kashmir, Srinagar 190006

Abstract

In this paper, we are concerned with the problem of locating the zeros of regular polynomials of a quaternionic variable with quaternionic coefficients. We derive new bounds of Enestr\"{o}m-Kakeya type for the zeros of these polynomials by virtue of a maximum modulus theorem and the structure of the zero sets in the newly developed theory of regular functions and polynomials of a quaternionic variable. Our results generalize some recently proved results about the distribution of zeros of a quaternionic polynomial.



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