ON ARGUMENT PROPERTY OF CERTAIN ANALYTIC FUNCTIONS

被引：0

作者：

Nunokawa, Mamoru ^{[1
]}

Bah, Alpha Mamadou ^{[2
]}

机构：

[1] Univ Gunma, Dept Math, Maebashi, Gunma 371, Japan

[2] Hiroshima Univ, Grad Sch Engn, Dept Appl Math, Hiroshima 7398527, Japan

来源：

STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA | 2010年 / 55卷 / 03期

关键词：

Univalent functions; Argument property of analytic functions;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we generalize the results of Libera and McGregor concerning argument property of analytic functions. We use the result in [3] to prove the following: Theorem. Let f(z) = z vertical bar Sigma(infinity)(n=p+K) a(n)z(n), g(z) = z vertical bar Sigma(infinity)(n=p+K) b(n)z(n) be analytic in Delta, f(z) not equal 0 in 0 < vertical bar z vertical bar < 1, and suppose that for some alpha, beta (0 < alpha < 1, 0 < beta < 1) vertical bar arg (f'(z)/g'(z)vertical bar < pi/2 alpha + Tan(-1) 2 alpha beta/1-beta(2) - Tan(-1) 2 alpha beta/(1-beta(2))root 1+alpha(2) in Delta, and taht g'(z)/zg(z) (sic) 1+beta z/1-beta z where (sic) means subordination. Then we have vertical bar arg(f(z)/g(z)vertical bar < pi/2 alpha in Delta.

引用

页码：163 / 168

页数：6

共 6 条

[1] SOME CLASSES OF REGULAR UNIVALENT FUNCTIONS [J].