Some refinements of Enestrom-Kakeya theorem

Abstract

In this paper we present certain interesting refinements of a well-known EnestromKakeya theorem in the theory of distribution of zeros of polynomials which among other things also improve upon some results of Aziz and Mohammad, Govil and Rehman and others.

Eneström–Kakeya Theorem and Some of Its Generalizations

“…In the same paper, Aziz and Zargar [9] proved a result related to Theorem 26, but with a hypothesis concerning the even-indexed and odd-indexed coefficients separately. Their result is:…”

“…With λ = a n−1 /a n , we see from Theorem 25 that the zeros of a polynomial with monotone coefficients a 0 ≤ a 1 ≤ · · · ≤ a n−1 has all its zeros in |z +(a n−1 /a n −1)| ≤ (a n−1 − a 0 + |a 0 |)/|a n |. Later, Aziz and Zargar [9] generalized their own Theorem 25 and proved:…”

“…Aziz and Zargar [9] relaxed the monotonicity condition of Joyal, Labelle, and Rahman [46] and obtained a result related to the Eneström-Kakeya theorem. Here,the disk obtained is not necessarily centered at the origin.…”

Bounds for the Zeros of a Polynomial with Restricted Coefficients

“…Let 1 1 ... Recently Aziz and Zarger [7] relaxed the hypothesis in several ways and among other things proved the following results:…”

On the Enestrom Kakeya Theorem

“…In the literature some attempts have been made to extend and generalize the Eneström-Kakeya Theorem. Aziz and Zargar [4] relaxed the hypothesis of Eneström-Kakeya theorem in a different way and proved the following results.…”