某些有界双分析函数和双调和映射的LANDAU-型定理

Pub Date : 2023-02-15 DOI:10.4153/s0008439523000577

Ming-Sheng Liu, S. Ponnusamy

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引用次数: 0

摘要

本文建立了$F(z)=\bar{z}G(z)+H(z)$的有界双解析函数的三个新版本的landau型定理，其中$G$和$H$在单位圆盘$|z|<1$上解析，$G(0)=H(0)=0$和$H'(0)=1$。其中两个是尖锐的，另一个是概括或改进了Abdulhadi和Hajj的相应结果。作为结果，证明了有界双调和映射的某些子类的朗道型定理的几个新的尖锐版本。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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LANDAU-TYPE THEOREMS FOR CERTAIN BOUNDED BI-ANALYTIC FUNCTIONS AND BIHARMONIC MAPPINGS

In this paper, we establish three new versions of Landau-type theorems for bounded bi-analytic functions of the form $F(z)=\bar{z}G(z)+H(z)$, where $G$ and $H$ are analytic in the unit disk $|z|<1$ with $G(0)=H(0)=0$ and $H'(0)=1$. In particular, two of them are sharp while the other one either generalizes or improves the corresponding result of Abdulhadi and Hajj. As consequences, several new sharp versions of Landau-type theorems for certain subclasses of bounded biharmonic mappings are proved.

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