Some Lp Inequalities for the Polar Deriv
β
N.K Govil; Griffith Nyuydinkong; Berhanu Tameru
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Article
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2001
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Elsevier Science
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English
β 95 KB
Let p n z be a polynomial of degree n and D Ξ± p n z its polar derivative. It has been proved that if p n z has no zeros in z < 1, then for Ξ΄ β₯ 1 and Ξ± β₯ 1, 2Ο 0 D Ξ± p n e iΞΈ Ξ΄ dΞΈ 1/Ξ΄ β€ n Ξ± + 1 F Ξ΄ 2Ο 0 p n e iΞΈ Ξ΄ dΞΈ 1/Ξ΄ where F Ξ΄ = 2Ο/ 2Ο 0 1 + e iΞΈ Ξ΄ dΞΈ 1/Ξ΄ . We also obtain analogous inequalities