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

Qinghua Xu; Taishun Liu; Xiaosong Liu

doi:10.1007/s11401-019-0184-y

Chinese Annals of Mathematics, Series B ›› 2020, Vol. 41 ›› Issue (1) : 37 -48. DOI: 10.1007/s11401-019-0184-y

Article

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

Qinghua Xu ¹^,^a
, Taishun Liu ²^,^b
, Xiaosong Liu ³^,^c

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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 ℂⁿ, which are natural extensions to higher dimensions of some Fekete and Szegö inequalities for subclasses of the normalized univalent functions in the unit disk.

Keywords

Coefficient inequality / Fekete-Szegö problem / Quasi-convex mappings

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Qinghua Xu, Taishun Liu, Xiaosong Liu. The Coefficient Inequalities for a Class of Holomorphic Mappings in Several Complex Variables. Chinese Annals of Mathematics, Series B, 2020, 41(1): 37-48 DOI:10.1007/s11401-019-0184-y