Gulshan Singh, Generalizations of Enestr¨om-Kakeya Theorem, Volume 2018, Number 1, Pages 109-119, 2018

# Gulshan Singh, Generalizations of Enestr¨om-Kakeya Theorem, Volume 2018, Number 1, Pages 109-119, 2018

Abstract: If $P(z):=\sum_{j=0}^{n} \alpha_{j}z^{j}$ be a polynomial of degree n such that $\alpha_{j}=a_{j}+ib_{j}$ where $a_{j}$ and $b_{j}$, j=0,1,...,n are real numbers. In this paper, we prove some extensions and generalizations of the classical results of the well known Enestr\"{o}m-Kakeya theorem by imposing restrictions on the complex coefficients of a polynomial in order to give bounds concerning the number of zeros in a specific region of the complex plane. Also, a variety of interesting results can be deduced from them by a uniform procedure.

Keywords: Polynomial, Zeros, Enestr\"{o}m-Kakeya theorem.