On concave univalent functions

被引：11

作者：

Bhowmik, Bappaditya ^{[1
]}

机构：

[1] Indian Inst Sci, Dept Math, Bangalore 560012, Karnataka, India

来源：

MATHEMATISCHE NACHRICHTEN | 2012年 / 285卷 / 5-6期

关键词：

Concave univalent functions; Taylor and Laurent coefficients; MSC (2010) 30C45; BOUNDED BOUNDARY ROTATION; COEFFICIENTS; SPACE;

D O I：

10.1002/mana.201000063

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider functions that map the open unit disc conformally onto the complement of an unbounded convex set with opening angle pa, a ? (1, 2], at infinity. In this paper, we show that every such function is close-to-convex of order (a - 1) and is included in the set of univalent functions of bounded boundary rotation. Many interesting consequences of this result are obtained. We also determine the extreme points of the set of concave functions with respect to the linear structure of the Hornich space.

引用

页码：606 / 612

页数：7

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