Pure and Applied Mathematics Quarterly

Volume 12 (2016)

Number 4

The Fekete and Szegö problem on bounded starlike circular domain in $\mathbb{C}^n$

Pages: 621 – 638

DOI: https://dx.doi.org/10.4310/PAMQ.2016.v12.n4.a9

Authors

Qinghua Xu (School of Science, Zhejiang University of Science and Technology, Hangzhou, China)

Taishun Liu (Department of Mathematics, Huzhou Teacher’s University, Huzhou, China)

Wenjun Zhang (College of Mathematics and Statistics, Shenzhen University, Shenzhen, China)

Abstract

In this paper, we establish the Fekete and Szegö inequality for a class of holomorphic mappings on the bounded starlike circular domain in $\mathbb{C}^n$, which is natural extension to higher dimensions of some classical Fekete and Szegö inequalities for various subclasses of the normalized univalent functions in the unit disk.

Keywords

Fekete-Szegö problem, bounded starlike circular domain, sharp coefficient bound

2010 Mathematics Subject Classification

Primary 32H02. Secondary 30C45.

Full Text (PDF format)

This work was supported by NNSF of China (Grant Nos. 11561030, 11261022, 11471111), by the Jiangxi Provincial Natural Science Foundation of China (Grant Nos. 20152ACB20002, 20161BAB201019), and bu the Natural Science Foundation of the Department of Education of Jiangxi Province, China (Grant No. GJJ150301).

Received 23 March 2017

Published 26 July 2018