A Note on Comparison of Annuli Containing all the Zeros of a Polynomial

Abstract

If P(z) is a polynomial of degree n, then for a subclass of polynomials, Dalal and Govil [7] compared the bounds, containing all the zeros, for two different results with two different real sequences λk > 0, Pn k=1 λk = 1. In this paper, we prove a more general result, by which one can compare the bounds of two different results with the same sequence of real or complex λk, Pn k=0 ♣λk♣ ≤ 1. A variety of other results have been extended in this direction, which in particular include several known extensions and generalizations of a classical result of Cauchy [4], from this result by a fairly uniform manner.