Generalization of an Eneström-Kakeya type theorem to the quaternions

Authors

  • Robert B. Gardner East Tennessee State University
  • Mariah Taylor East Tennessee State University

DOI:

https://doi.org/10.52737/18291163-2022.14.9-1-8

Keywords:

Location of Zeros of a Polynomial, Eneström-Kakeya Theorem, Quaternionic Polynomial

Abstract

The well-known Eneström-Kakeya theorem states that polynomial $p(z)=\sum_{\nu =0}^n a_\nu z^\nu$, where $0\leq a_0\leq a_1\leq \cdots\leq a_n$, has all of its (complex) zeros in $|z|\leq 1$. Many generalizations of this result exist in the literature. In this paper, we extend one such result to the quaternionic setting and state one of the possible corollaries.

References

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Published

2022-06-29

How to Cite

Gardner, R. B., & Taylor, M. (2022). Generalization of an Eneström-Kakeya type theorem to the quaternions. Armenian Journal of Mathematics, 14(9), 1–8. https://doi.org/10.52737/18291163-2022.14.9-1-8