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Inequalities for the Polar Derivative of a Polynomial

✍ Scribed by A. Liman, R. N. Mohapatra, W. M. Shah

Book ID
118818467
Publisher
SP Birkhäuser Verlag Basel
Year
2010
Tongue
English
Weight
177 KB
Volume
6
Category
Article
ISSN
1661-8254

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Some Lp Inequalities for the Polar Deriv
Some Lp Inequalities for the Polar Derivative of a Polynomial
✍ N.K Govil; Griffith Nyuydinkong; Berhanu Tameru 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 95 KB

Let p n z be a polynomial of degree n and D α p n z its polar derivative. It has been proved that if p n z has no zeros in z < 1, then for δ ≥ 1 and α ≥ 1, 2π 0 D α p n e iθ δ dθ 1/δ ≤ n α + 1 F δ 2π 0 p n e iθ δ dθ 1/δ where F δ = 2π/ 2π 0 1 + e iθ δ dθ 1/δ . We also obtain analogous inequalities