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An Lp Inequality for a Polynomial and Its Derivative

โœ Scribed by R.B. Gardner; N.K. Govil

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
191 KB
Volume
194
Category
Article
ISSN
0022-247X

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๐Ÿ“œ SIMILAR VOLUMES

Some Lp Inequalities for the Polar Deriv
Some Lp Inequalities for the Polar Derivative of a Polynomial
โœ N.K Govil; Griffith Nyuydinkong; Berhanu Tameru ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 95 KB

Let p n z be a polynomial of degree n and D ฮฑ p n z its polar derivative. It has been proved that if p n z has no zeros in z < 1, then for ฮด โ‰ฅ 1 and ฮฑ โ‰ฅ 1, 2ฯ€ 0 D ฮฑ p n e iฮธ ฮด dฮธ 1/ฮด โ‰ค n ฮฑ + 1 F ฮด 2ฯ€ 0 p n e iฮธ ฮด dฮธ 1/ฮด where F ฮด = 2ฯ€/ 2ฯ€ 0 1 + e iฮธ ฮด dฮธ 1/ฮด . We also obtain analogous inequalities