An annulus for the zeros of polynomials

Bidkham, M.; Shashahani, E.

doi:10.1016/j.aml.2010.08.030

Cited by 8 publications

(5 citation statements)

References 5 publications

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“…There are many results, including the above Theorems 1.3 and 1.4, available in this direction (for example, see [3,5,10]).…”

Section: Here C(n K) Is the Binomial Coefficientmentioning

confidence: 99%

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

Hans¹,

Tomar²,

CHEN³

2022

KgJMat

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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.

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“…There are many results, including the above Theorems 1.3 and 1.4, available in this direction (for example, see [3,5,10]).…”

Section: Here C(n K) Is the Binomial Coefficientmentioning

confidence: 99%

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

Hans¹,

Tomar²,

CHEN³

2022

KgJMat

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“…There are in fact many results in this direction, and for some more results, see, for example, [13,14].…”

Section: Theorem 5 Let ( ) = ∑ =0mentioning

confidence: 99%

Annular Bounds for the Zeros of a Polynomial

Gao

Govil

2018

International Journal of Mathematics and Mathematical Sciences

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The problem of obtaining the smallest possible region containing all the zeros of a polynomial has been attracting more and more attention recently, and in this paper, we obtain several results providing the annular regions that contain all the zeros of a complex polynomial. Using MATLAB, we construct specific examples of polynomials and show that for these polynomials our results give sharper regions than those obtainable from some of the known results.

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“…There are many results, including the above Theorems 1.3 and 1.4, available in this direction (for example, see [3,5,10,11,12,16,23]).…”

Section: Introductionmentioning

confidence: 99%

On comparison of annuli containing all the zeros of a polynomial

Dalal

Govil

2017

APPL ANAL DISCRETE M

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There are many theorems providing annulus containing all the zeros of a polynomial, and it is known that two such theorems cannot be compared, in the sense that one can always find a polynomial for which one theorem gives a sharper bound than the other. It is natural to ask if there is a class of polynomials for which such comparison is possible and in this paper we investigate this problem and provide results which for polynomials with some condition on the degree or absolute range of coefficients, enable us to compare two such theorems.

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An annulus for the zeros of polynomials

Cited by 8 publications

References 5 publications

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

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

Annular Bounds for the Zeros of a Polynomial

On comparison of annuli containing all the zeros of a polynomial

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