ON THE WEAKENED HYPOTHESES-BASED GENERALIZATIONS OF THE ENESTRÖM-KAKEYA THEOREM

According to the well-known Eneström-Kakeya Theorem, all the zeros of a polynomial $P(z)={\sum_{s=0}^{n}}a_sz^s$ of degree n with real coefficients satisfying a_n ≥ a_n-1 ≥ · · · ≥ a₁ ≥ a₀ > 0 lie in the complex plane |z| ≤ 1. We provide comparable results with hypotheses relating to the real and imaginary parts of the coefficients as well as the coefficients' moduli in response to recent findings about an Eneström-Kakeya "type" condition on real coefficients. Our findings so broadly extend the other previous findings.