Functions of Exponential Type Not Vanishing in a Half-Plane and Related Polynomials

Govil, N. K.; Rahman, Q. I.

doi:10.2307/1994818

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\K=0 J K=01

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2019

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Cited by 20 publications

(19 citation statements)

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“…The Inequality (1.3) is also best possible and equality holds for P (z) = a + bz n , where |a| = |b|. The generalization of the Inequality (1.3) to class of polynomials having no zeros in |z| < K, K ≥ 1 was done by Malik [14] (See also Govil and Rahman [10,Theorem 4]), who proved that, if a polynomial P (z) of degree n has no zeros in |z| < K, K ≥ 1, then…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

On sharpening of an inequality of Turán

Govil

Kumar

2019

Appl Anal Discrete Math

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Let P (z) = n ν=0 aν z ν be a polynomial of degree n. Then as a generalization of a well-known result of Turán [18], it was proved by Govil [5] that if P (z) is a polynomial of degree n having all its zeros in |z| ≤ K, K ≥ 1, then (0.1) max |z|=1 |P (z)| ≥ n 1 + K n max |z|=1 |P (z)|. In this paper, we prove a polar derivative generalization of this inequality, which as a corollary gives a sharpening of this inequality (0.1).

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Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

On sharpening of an inequality of Turán

Govil

Kumar

2019

Appl Anal Discrete Math

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show abstract

“…The result is best possible and equality in (5) holds for p n z = λ + µz n , where µ = λ and α ≥ 1 Remark 1.1. If we divide both sides of (5) by α and make α → ∞ we get inequality (2) due to Lax [7].…”

Section: Introductionmentioning

confidence: 99%