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).
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页码：291 / 302
页数：12
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