The Coefficient Inequalities for a Class of Holomorphic Mappings in Several Complex Variable

Citation:

Qinghua XU,Taishun LIU,Xiaosong LIU.The Coefficient Inequalities for a Class of Holomorphic Mappings in Several Complex Variable[J].Chinese Annals of Mathematics B,2020,41(1):37~48
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Authors:

Qinghua XU; Taishun LIU;Xiaosong LIU

Foundation:

This work was supported by the National Natural Science Foundation of China (Nos.11971165, 11561030, 11471111), the Jiangxi Provincial Natural Science Foundation of China (Nos.20152ACB20002, 20161BAB201019) and the Natural Science Foundation of Department of Education of Jiangxi Province of China (No.GJJ150301).
Abstract: The authors establish the coefficient inequalities for a class of holomorphic mappings on the unit ball in a complex Banach space or on the unit polydisk in $\mathbb{C}^n$, which are natural extensions to higher dimensions of some Fekete and Szeg\"o inequalities for subclasses of the normalized univalent functions in the unit disk.

Keywords:

Coefficient inequality, Fekete-Szeg"{o} problem, Quasi-convex mappings

Classification:

32H02, 30C45
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