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Some integral inequalities for the polar derivative of a polynomial

✍ Scribed by Abdullah Mir; Sajad Amin Baba


Book ID
113061126
Publisher
Springer
Year
2011
Tongue
English
Weight
111 KB
Volume
27
Category
Article
ISSN
1573-8175

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πŸ“œ SIMILAR VOLUMES


Some Lp Inequalities for the Polar Deriv
✍ N.K Govil; Griffith Nyuydinkong; Berhanu Tameru πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 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΄ ≀ 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