Some Lp Inequalities for the Polar Derivative of a Polynomial

Govil, N. K.; Nyuydinkong, Griffith; Tameru, Berhanu

doi:10.1006/jmaa.2000.7267

Cited by 10 publications

(7 citation statements)

References 13 publications

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“…Here we shall also present a correct proof of Theorem 2, which shall validate Theorems 1.2 and 1.3 of Govil et al [5] as well. Finally we shall also present a short proof of Theorem 1.3 of [5].…”

Section: Theorem 2 If P(z) Is a Polynomial Of Degree N Which Does Nosupporting

confidence: 73%

“…which clearly contradicts (5). Hence inequality (4) is not, in general, true for all polynomials P(z) of degree n ≥ 1.…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 87%

“…While seeking the desired extension to the polar derivatives, recently Govil et al [5] have made an incomplete attempt by claiming to have proved the following generalization of ( 11) and ( 14).…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

“…If we divide both sides of (14) by |α| and make |α| → ∞, we get inequality (13) due to Lax [6]. While seeking the desired extension to the polar derivatives, recently Govil et al [5] have made an incomplete attempt by claiming to have proved the following generalization of (11) and (14).…”

Section: Theorem 1 If P(z) Is a Polynomial Of Degree N Then For Evementioning

confidence: 99%

“…and use the same argument as used by Govil et al (page 624, line 10 of [5]), then in view of the inequality for every p ≥ 1 and |α| ≥ 1, which is not true in general as shown above.…”

Section: Theorem 2 If P(z) Is a Polynomial Of Degree N Which Does Nomentioning

confidence: 99%

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On an inequality concerning the polar derivative of a polynomial

Aziz

Rather

2007

Proc Math Sci

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Section: Theorem 2 If P(z) Is a Polynomial Of Degree N Which Does Nosupporting

confidence: 73%

“…which clearly contradicts (5). Hence inequality (4) is not, in general, true for all polynomials P(z) of degree n ≥ 1.…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 87%

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

Section: Theorem 1 If P(z) Is a Polynomial Of Degree N Then For Evementioning

confidence: 99%

“…and use the same argument as used by Govil et al (page 624, line 10 of [5]), then in view of the inequality for every p ≥ 1 and |α| ≥ 1, which is not true in general as shown above.…”

Section: Theorem 2 If P(z) Is a Polynomial Of Degree N Which Does Nomentioning

confidence: 99%

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