多复变一类星形映照子族的系数不等式

郭盛梯, 徐庆华

doi:10.13371/j.cnki.chin.q.j.m.2018.01.012

数学季刊 >

2018 , Vol. 33 >Issue 1: 98 - 110

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2018.01.012

多复变一类星形映照子族的系数不等式

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College of Mathematics and Information Science, Jiang Xi Normal, Jiang Xi Normal University. School of Science, Zhejiang University of Science and Technology

GUO Sheng-ti(1993-), male, native of Huangshi, Hubeia master of mathematics of JiangXi Normal Universityengages in complex analysis; XU Qing-hua (corresponding author)(1970-) male, native of Chaohu, Anhui, a professor of Zhejiang University of Science and Technology,Ph.D.,engages in complex analysis.

收稿日期: 2018-01-10

网络出版日期: 2020-10-19

基金资助

supported by NNSF of China(Grant Nos.11561030,11261022)； the Jiangxi Provincial Natural Science Foundation of China(Grant Nos.20152ACB20002,20161BAB201019)； Natural Science Foundation of Department of Education of Jiangxi Province,China(Grant No.GJJ150301)； the Jiangxi Provincial graduate student innovation project(Grant No.YC2016-S159)；

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On the Cofficient Inequality for A Subclass of Starlike Mappings in Several Complex Variables

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College of Mathematics and Information Science, Jiang Xi Normal, Jiang Xi Normal University. School of Science, Zhejiang University of Science and Technology

Received date: 2018-01-10

Online published: 2020-10-19

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摘要

Let S^* be the familiar class of normalized univalent functions in the unit disk.In [9], Keogh and Merkes proved that for a function f（z） = z +∑k=2∞ a_kz^kin the class S^*,then |a₃-λa_2^2| ≤ max{1, |3-4λ|}, λ∈ C. In this article, we investigate the corresponding problem for the subclass of starlike mappings defined on the unit ball in a complex Banach space, on the unit polydisk in Cⁿand the bounded starlike circular domain in C^*, respectively.

关键词： Fekete-Szeg?o problem; Subclass of starlike mappings; Sharp coefficient bound

本文引用格式

郭盛梯, 徐庆华 . 多复变一类星形映照子族的系数不等式[J]. 数学季刊, 2018 , 33(1) : 98 -110 . DOI: 10.13371/j.cnki.chin.q.j.m.2018.01.012

Abstract

Key words： Fekete-Szeg?o problem; Subclass of starlike mappings; Sharp coefficient bound

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