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

GUO Sheng-ti, XU Qing-hua

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

Chinese Quarterly Journal of Mathematics >

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

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

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

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.

Received date: 2018-01-10

Online published: 2020-10-19

Supported by

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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Abstract

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.

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

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GUO Sheng-ti, XU Qing-hua . On the Cofficient Inequality for A Subclass of Starlike Mappings in Several Complex Variables[J]. Chinese Quarterly Journal of Mathematics, 2018 , 33(1) : 98 -110 . DOI: 10.13371/j.cnki.chin.q.j.m.2018.01.012

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