Bounds for the Zeros of a Polynomial with Restricted Coefficients

Abstract

In this paper we shall obtain some interesting extensions and generalizations of a well-known theorem due to Enestrom and Kakeya according to which all the zeros of a polynomial  

On the location of zeros of a polynomial with restricted coefficients

“…In the literature [1][2][3][4][5][6][7][8][9][10][11] there exist several extensions and generalizations of this theorem. Joyal et al [9] extended Theorem A to the polynomials whose coefficients are monotonic but not necessarily non-negative.…”

Eneström–Kakeya Theorem and Some of Its Generalizations

“…In 2012, Aziz and Zargar [10] modified the hypotheses of their own 1996 result, Theorem 25, and proved the following three theorems.…”

“…Aziz and Zargar [10] also showed that each of these implies Theorem 7 of Joyal, Labelle, and Rahman, and hence it is a generalization of the Eneström-Kakeya theorem. Recently, Gulzar [33] (see also [31]) proved:…”

Some generalizations of the Eneström–Kakeya theorem

“…In 2012, they further generalized Theorem C which is an interesting extension of Theorem A. In particular, they [3] proved the following results:…”