| B~n上推广的Roper-Suffridge算子的性质 |
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| 引用本文： | 王朝君,崔艳艳,刘浩.B~n上推广的Roper-Suffridge算子的性质[J].数学学报,2016,59(6):729-744. |
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| 作者姓名： | 王朝君 崔艳艳 刘浩 |
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| 作者单位： | 1. 周口师范学院数学与统计学院 周口 466001;
2. 河南大学数学与统计学院 开封 475001 |
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| 基金项目： | 国家自然科学基金资助项目（U1204618）；河南省教育厅科学技术研究重点项目（14B110016） |
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| 摘 要： | 讨论改进后的Roper-Suffridge延拓算子保持双全纯映照子族的性质.借助双全纯映照子族的解析特征及其偏差结论,得到改进后的Roper-Suffridge延拓算子在一定条件下保持α次殆β型螺形映照、α次β型螺形映照、强β型螺形映照的性质,从而得到改进后的算子在一定条件下保持α次殆星形性、α次星形性和强星形性.所得结论为在多复变数空间中构造这些双全纯映照提供了一种新的途径.
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| 关 键 词： | Roper-Suffridge延拓算子 螺形映照 星形映照 |
Property of the Modified Roper-Suffridge Extension Operators on Bn |
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| Chao Jun WANG,Yan Yan CUI,Hao LIU.Property of the Modified Roper-Suffridge Extension Operators on Bn[J].Acta Mathematica Sinica,2016,59(6):729-744. |
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| Authors: | Chao Jun WANG Yan Yan CUI Hao LIU |
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| Institution: | 1. College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, P. R. China;
2. College of Mathematics and Statistics, He'nan University, Kaifeng 475001, P. R. China |
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| Abstract: | We mainly discuss the property of the modified Roper-Suffridge operators. By the analytical characteristics and distortion results of subclasses of biholomorphic mappings, we conclude that the modified Roper-Suffridge operators preserve almost spirallikeness of order α and type β, spirallikeness of order α and type β, strong spiral-likeness of type β on Bn, respectively. Sequentially, we get that the modified Roper-Suffridge operators preserve almost starlikeness of order α, starlikeness of order α and strong starlikeness on Bn. The conclusions provide a new approach to construct these biholomorphic mappings in several complex variables. |
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| Keywords: | Roper-Suffridge operator spirallike mappings starlike mappings |
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