On the Biholomorphic Convex Mappings of Order Alpha on \(D_p^n\)

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• 作者：Ming-Sheng Liu ; Ni Li ; Yan Yang
• 关键词：Locally biholomorphic mapping ; Biholomorphic convex mapping ; Biholomorphic convex mapping of order \(\alpha \) ; Reinhardt domain \(D_{p}^n\)
• 刊名：Complex Analysis and Operator Theory
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：11
• 期：2
• 页码：243-260
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general; Operator Theory; Analysis;
• 出版者：Springer International Publishing
• ISSN：1661-8262
• 卷排序：11

文摘

In this paper, we first give the definition of biholomorphic convex mappings of order \(\alpha \) on the Reinhardt domain \(D_{p}^n\) in \(C^{n}\). Next, we provide several sufficient conditions for it. Then we introduce a subclass \(SK(D_{p}^n, \alpha )\) of biholomorphic convex mappings of order \(\alpha \) on \(D_{p}^n\), and give a necessary and sufficient condition for the subclass \(SK(D_{p}^n, \alpha )\). From these, we construct some concrete examples of biholomorphic convex mappings of order \(\alpha \) on \(D_{p}^n\). The results presented extend the related results of earlier authors.