Some Generalizations of the Enestr\"om-Kakeya Theorem

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.