Some Generalizations of the Enestr\"om-Kakeya Theorem

TL;DR

This paper extends and generalizes the Enestr"om-Kakeya Theorem by imposing restrictions on polynomial coefficients, providing broader conditions under which the theorem's conclusions hold.

Contribution

It introduces new generalizations of the Enestr"om-Kakeya Theorem for polynomials with real coefficients under specific restrictions.

Findings

Extended conditions for polynomial zeros

Broader applicability of the Enestr"om-Kakeya Theorem

New theoretical bounds on zeros of polynomials

Abstract

Let $p(z)=a_0+a_1z+a_2z^2+a_3z^3+\cdots+a_nz^n$ be a polynomial of degree $n,$ where the coefficients $a_j,$ $j \in \{0,1,2,\cdots n\},$ are real numbers. We impose some restriction on the coefficients and then prove some extensions and generalizations of the Enestr\"{o}m-Kakeya Theorem.