UNIFIED SOLUTION OF FEKETE-SZEGO PROBLEM FOR SUBCLASSES OF STARLIKE MAPPINGS IN SEVERAL COMPLEX VARIABLES

被引：23

作者：

Tu, Zhenhan ^{[1
]}

Xiong, Liangpeng ^{[1
]}

机构：

[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China

来源：

MATHEMATICA SLOVACA | 2019年 / 69卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Bounded starlike circular domain; Fekete-Szego problem; Minkowski functional; starlike mappings; subordination; COEFFICIENT BOUNDS; GROWTH; INEQUALITY;

D O I：

10.1515/ms-2017-0273

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let S-phi* be a subclass of starlike functions in the unit disk U; where phi is a convex function such that phi(0) = 1, phi'(0) > 0, R(phi(xi)) > 0 and phi(U) is symmetric with respect to the real axis. We obtain the sharp solution of Fekete-Szego problem for the family S-phi*, and then extend the result to the case of corresponding subclass defined on the bounded starlike circular domain Omega in several complex variables, which give an unified answer of Fekete-Szego problem for the kinds of subclasses of starlike mappings de fined on Omega. At last, we propose two conjectures related the same problems on the unit ball in a complex Banach space and on the unit polydisk in C-n. (C) 2019 Mathematical Institute Slovak Academy of Sciences

引用

页码：843 / 856

页数：14

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