Some generalizations of the Eneström–Kakeya theorem

Abstract

Let p(z) = a₀ + a₁z + a₂z² + ... + a_nzⁿ be a polynomial of degree n; where the coefficients a_j, j = 0, 1, 2, ..., n, are real numbers. We impose some restriction on the coefficients and then prove some extensions and generalizations of the Eneström–Kakeya theorem.