STARLIKENESS AND CONVEXITY OF CAUCHY TRANSFORMS ON REGULAR POLYGONS

被引：0

作者：

Zhang, Peng-Fei ^{[1
]}

Dong, Xin-Han ^{[1
]}

机构：

[1] Hunan Normal Univ, Coll Math & Stat, Minist Educ China, Key Lab High Performance Comp & Stochast Informat, Changsha, Hunan, Peoples R China

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2021年 / 103卷 / 02期

关键词：

starlikeness convexity; univalence; Cauchy transform; regular polygons;

D O I：

10.1017/S0004972720000696

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For n >= 3, let Q(n) subset of C be an arbitrary regular n-sided polygon. We prove that the Cauchy transform F-Qn of the normalised two-dimensional Lebesgue measure on Q(n) is univalent and starlike but not convex in (C) over cap \Q(n).

引用

页码：291 / 302

页数：12

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