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.

引用

页码：1199 / 1209

页数：11

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