On inequalities involving polar derivative of a polynomial

被引：19

作者：

Govil, N. K. ^{[1
]}

Kumar, P. ^{[2
,3
]}

机构：

[1] Auburn Univ, Dept Math & Stat, Auburn, AL 36849 USA

[2] Birla Inst Technol & Sci Pilani, Dept Math, KK Birla Goa Campus, Sancoale 403726, Goa, India

[3] Auburn Univ, Auburn, AL 36849 USA

来源：

ACTA MATHEMATICA HUNGARICA | 2017年 / 152卷 / 01期

关键词：

polynomial; zero; L-p inequality;

D O I：

10.1007/s10474-017-0693-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that if P(z) is a polynomial of degree n with zeros z (m) , that satisfy , , then for any p > 0, and for every complex number alpha, with , we have where , and if , and t (0) = 1 if K (m) = 1 for some m, . Our results generalize and sharpen several of the known results.

引用

页码：130 / 139

页数：10

共 15 条

[1]

[Anonymous], 2008, J INEQ PURE APPL MAT

[2]

[Anonymous], 1947, NEDERL AKAD WETENSCH

[3]

Arestov V. V., 1981, Izv. Akad. Nauk. SSSR. Ser. Math., V45, P3

[4] INEQUALITIES FOR THE POLAR DERIVATIVE OF A POLYNOMIAL [J].