The estimates of all homogeneous expansions for a subclass of biholomorphic mappings which have parametric representation in several complex variables

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• 作者：Xiao Song Liu ; Tai Shun Liu
• 关键词：Estimate of homogeneous expansion ; starlike mapping ; starlike mapping of order α ; quasi ; convex mapping ; quasi ; convex mapping of type A ; parametric representation
• 刊名：Acta Mathematica Sinica, English Series
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：33
• 期：2
• 页码：287-300
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
• ISSN：1439-7617
• 卷排序：33

文摘

In this paper, we obtain the estimates of all homogeneous expansions for a subclass of biholomorphic mappings which have parametric representation on the unit ball of complex Banach spaces. Meanwhile, we also establish the estimates of all homogeneous expansions for the above generalized mappings on the unit polydisk in Cn. Especially, the above estimates are only sharp for biholomorphic starlike mappings and starlike mappings of order α under restricted conditions. Our derived results generalize many known results.