English

Quaternionic Generalization of the Enestr\"{o}m-Kakeya Theorem

Complex Variables 2025-03-12 v1

Abstract

{In 2020, Carney et.al. proved the quaternionic version of the Enestr\"{o}m-Kakeya Theorem, which states that a polynomial p(q)=ν=0nqνaνp(q)=\sum_{\nu=0}^n q^\nu a_\nu with non-negative and monotonically increasing coefficients (0<a0a1an)(0<a_0\le a_1\le \cdots \le a_n) has all of its zeros within the unit ball q1|q|\le 1. Numerous generalizations of Enestr\"{o}m-Kakeya Theorem are available in the literatures (\cite{m}-\cite{mmr}). In this paper, we extend some of these generalizations to the quaternionic context and present several potential results.}

Keywords

Cite

@article{arxiv.2503.08618,
  title  = {Quaternionic Generalization of the Enestr\"{o}m-Kakeya Theorem},
  author = {D. Tripathi},
  journal= {arXiv preprint arXiv:2503.08618},
  year   = {2025}
}

Comments

10 pages

R2 v1 2026-06-28T22:16:13.545Z