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Some polynomial inequalities in the complex domain

✍ Scribed by K. K. Dewan; S. Hans

Publisher
Springer
Year
2010
Tongue
English
Weight
76 KB
Volume
26
Category
Article
ISSN
1573-8175

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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