Inequalities for the Polar Derivative of a Polynomial

被引：15
|
作者：
Liman, A. [1 ]
Mohapatra, R. N. [2 ]
Shah, W. M. [3 ]
机构：
[1] Natl Inst Technol, Dept Math, Srinagar 190006, Kashmir, India
[2] Univ Cent Florida, Dept Math, Orlando, FL 32817 USA
[3] Univ Kashmir, Dept Math, Srinagar 190006, Jammu & Kashmir, India
来源：
COMPLEX ANALYSIS AND OPERATOR THEORY | 2012年 / 6卷 / 06期
关键词：
Polynomials; Polar derivative; Inequalities in the complex domain;
D O I：
10.1007/s11785-010-0120-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let P(z) be a polynomial of degree at most n. We consider an operator D (alpha) which maps a polynomial P(z) into D (alpha) P(z) := nP(z) + (alpha - z)P'(z) and prove results concerning the estimates of |D (alpha) P(z)| on the disk |z| = R a parts per thousand yen 1, and thereby obtain extensions and generalizations of a number of well-known polynomial inequalities.
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页码：1199 / 1209
页数：11
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