TITLE:
A Generalization of Eneström-Kakeya Theorem and a Zero Free Region of a Polynomial
AUTHORS:
Mushtaq Ahmad Shah, Ram Swroop, Humayun Mohd Sofi, Insha Nisar
KEYWORDS:
Polynomial, Zeros, Eneström-Kakeya Theorem
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.9 No.6,
June
18,
2021
ABSTRACT: For the polynomial P (z) = ajzj, aj ≥ aj-1, a0 > 0, j = 1, 2, …, n, an > 0, a classical result of Eneström-Kakeya says that all the zeros of P (z) lie in |z|≤ 1. This result was generalised by A. Joyall and G. Labelle, where they relaxed the non-negativity condition on coefficients. It was further generalized by M.A Shah by relaxing the monotonicity of some coefficients. In this paper, we use some known techniques and provide some more generalizations of the above results by giving more relaxation to the conditions.