Some Zygmund type Lq inequalities for polynomials

Aziz, Abdul; Rather, N. A.

doi:10.1016/s0022-247x(03)00530-4

Cited by 40 publications

(12 citation statements)

References 12 publications

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“…where as the corresponding extension of (1. 3) and a refinement of (1.4) was given by Govil [12] who under the same hypothesis proved that…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 76%

On Polynomials and Their Polar Derivative

Mir¹

2016

Mathematical Sciences and Applications E-Notes

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Let P (z) be a polynomial of degree n and for any complex number α, let D α P (z) = nP (z) + (α − z)P (z) denote the polar derivative of P (z) with respect to α. Here, we consider the class of polynomials P (z) = a n z n + n ν=µ a n−ν z n−ν , 1 ≤ µ ≤ n, having all zeros in |z| ≤ k, k ≤ 1 and thereby establish several interesting results regarding the integral mean estimates for the polar derivative of P (z). Our results not only generalize and refine some known polynomial inequalities, but also a variety of interesting results can be deduced from these by a fairly uniform procedure.

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“…where as the corresponding extension of (1. 3) and a refinement of (1.4) was given by Govil [12] who under the same hypothesis proved that…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 76%

On Polynomials and Their Polar Derivative

Mir¹

2016

Mathematical Sciences and Applications E-Notes

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“…Inequality (1.11) was extended to L γ norm by Aziz and Rather [2]. They proved that if p ∈ P n has no zero in |z| < k, k ≥ 1, then for each γ > 0…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

$L^{\gamma}$ INEQUALITIES CONCERNING POLYNOMIALS

Krishnadas¹,

Chanam²

2021

Int. J. of Appl. Math.

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“…A result due to Aziz and Rather [4,Corollary 5] is a special case of Corollary 2 when β = 0. Also using the fact that 1 ≤ t k,μ ≤ k μ , 1 ≤ μ ≤ n, we conclude that Corollary 2 is a refinement of a result due to Aziz and Shah [5], when β = 0.…”

Section: Introductionmentioning

confidence: 94%

Integral Mean Estimates for a Polynomial with Restricted Zeros

Liman¹,

Shah²

2014

Trends in Mathematics

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Let P n be the class of polynomials P (z) = n j =0 a j z j of degree n. For P ∈ P n , defineandIt was shown by Turan [14], that if P ∈ P n and P (z) has all its zeros in |z| ≤ 1, thenThe result is best possible and equality holds for P (z) = αz n +β, where |α| = |β|. As a generalization of inequality (11.1), Malik [12] proved that if P ∈ P n and P (z) = 0 in |z| ≤ k, where k ≤ 1 thenThe result is best possible and equality holds for P (z) = (z + k) n .A. Liman ( )

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Some Zygmund type Lq inequalities for polynomials

Cited by 40 publications

References 12 publications

On Polynomials and Their Polar Derivative

On Polynomials and Their Polar Derivative

$L^{\gamma}$ INEQUALITIES CONCERNING POLYNOMIALS

Integral Mean Estimates for a Polynomial with Restricted Zeros

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