On the Location of Zeros of Polynomials

Singh, Gurkirat; Shah, W. M.

doi:10.4236/ajcm.2011.11001

Cited by 5 publications

(4 citation statements)

References 16 publications

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“…In the same paper, Singh and Shah [59] introduced a reversal in the inequality imposed on the coefficients at a particular point and proved:…”

Section: Again This Results Implies Aziz and Mohammad's Theorem 15mentioning

confidence: 99%

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Eneström–Kakeya Theorem and Some of Its Generalizations

Gardner

Govil

2014

Trends in Mathematics

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“…In the same paper, Singh and Shah [59] introduced a reversal in the inequality imposed on the coefficients at a particular point and proved:…”

Section: Again This Results Implies Aziz and Mohammad's Theorem 15mentioning

confidence: 99%

“…Using the same hypotheses as Theorem 35, Singh and Shah [59] proved another result concerning the location of zeros, but this time obtained an annulus region containing all the zeros:…”

Section: Again This Results Implies Aziz and Mohammad's Theorem 15mentioning

confidence: 99%

Eneström–Kakeya Theorem and Some of Its Generalizations

Gardner

Govil

2014

Trends in Mathematics

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“…In the literature (see, e.g., [6,7,14,21]), one can nd several modi cations and generalizations of the above recalled result. In fact, even some considerations already exist which extend this classical result to the case of matrix polynomials (see, e.g., [8,23]).…”

Section: Introductionmentioning

confidence: 88%

On some special polynomials appearing in orthogonal systems on the unit circle

Lasarow

2014

Analysis

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A classical theorem due to Eneström and Kakeya gives some bounds for the moduli of the zeros of polynomials having a monotone sequence of nonnegative (real) coe cients. Nowadays, one can nd several modi cations and generalizations of this result in the literature. The main subject of the paper is a study of links of coe cients which occur in some of these general results with a view to the recurrence relations ful lled by systems of orthogonal polynomials on the unit circle. In particular, we discuss the question, if the relevant links are consistent with the recurrence relations or not. This leads to some new insight into the analyzed classes of polynomials.

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“…Some results for locating the latent roots are extended from well known results for complex polynomials [5,24]. Nowadays some results for complex polynomials are still being obtained [7,9,12,22,30,34].…”

Section: Localization and Upper Bounds For The Zeros Of Unilateral Octonionic Polynomialsmentioning

confidence: 99%

Bounds for the zeros of unilateral octonionic polynomials

Serôdio

Beites

Vitória

2021

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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In the present work it is proved that the zeros of a unilateral octonionic polynomial belong to the conjugacy classes of the latent roots of an appropriate lambda-matrix. This allows the use of matricial norms, and matrix norms in particular, to obtain upper and lower bounds for the zeros of unilateral octonionic polynomials. Some results valid for complex and/or matrix polynomials are extended to octonionic polynomials.

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On the Location of Zeros of Polynomials

Abstract: In this paper, we prove some extensions and generalizations of the classical Eneström-Kakeya theorem

Cited by 5 publications

References 16 publications

Eneström–Kakeya Theorem and Some of Its Generalizations

Eneström–Kakeya Theorem and Some of Its Generalizations

On some special polynomials appearing in orthogonal systems on the unit circle

Bounds for the zeros of unilateral octonionic polynomials

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