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On spirallike mappings in Several Complex Variables

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Chinese Quarterly Journal of Mathematics 1999年第1期14卷 62-72,页

作者：刘浩中国科学技术大学安徽合肥 2 3 0 0 2

In this paper,the parametric representation of a kind of spirallike mappings is given. As a direct application,the growth Theorem is set up. Moreover,a character of starlike mappings and a kind of spirallike mappings ... 详细信息

关键词： spirallike mappings parametric representation growth theorem

A Note of spirallike mappings in C^n

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Chinese Quarterly Journal of Mathematics 1999年第1期14卷 52-54,页

作者：李小申洛阳工学院河南洛阳 471 0 00

In this paper,the Growth and covering Theorems for a kind of spirallike mapping are given.

关键词： spirallike mappings Growth Theorems normal matrix

THE EXTENSION OPERATORS ON Bn+1 AND BOUNDED COMPLETE REINHARDT DOMAINS

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Acta Mathematica Scientia 2020年第5期40卷 1271-1288页

作者： Yanyan CUI Chaojun WANG Hao LIU College of Mathematics and Statistics Zhoukou Normal UniversityZhoukou 466001China Institute of Contemporary Mathematics Henan UniversityKaifeng 475001China

In this article, we extend the well-known Roper-Suffridge operator on Bn+1 and bounded complete Reinhardt domains in Cn+1, then we investigate the properties of the generalized operators. Applying the Loewner theory, we obtain the mappings constructed by the generalized operators that have parametric representation on Bn+1. In addition, by using the geometric characteristics and the parametric representation of subclasses of spirallike mappings, we conclude that the extended operators preserve the geometric properties of several subclasses of spirallike mappings on Bn+1 and bounded complete Reinhardt domains in Cn+1. The conclusions provide new approaches to construct mappings with special geometric properties in Cn+1.

关键词： Roper-Suffridge operator Reinhardt domains spirallike mappings

THE GENERALIZED ROPER-SUFFRIDGE OPERATOR ON THE UNIT BALL IN COMPLEX BANACH AND HILBERT SPACES

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Acta Mathematica Scientia 2017年第6期37卷 1817-1829页

作者：崔艳艳王朝君刘浩 College of Mathematics and Information Science Hebei Normal University College of Mathematics and Statistics Zhoukou Normal University Institute of Contemporary Mathematics Henan University

In this paper, we extend the Roper-Suffridge extension operator in complex Ba- nach space, and prove that the extended Roper-Suffridge operators preserve the properties of the subclasses of spirallike mappings on the unit bM1 in complex Banach spaces. Thereby, we promote the conclusions to the cases in complex Hilbert spaces. The conclusions provide new approaches to construct these subclasses of spiraJlike mappings in several complex variables.

关键词： spirallike mappings starlike mappings Roper-Suffridge operator

Extension Operators Preserving Biholomorphic mappings on Hartogs Domains

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Chinese Annals of Mathematics,Series B 2023年第2期44卷 307-324页

作者： Yanyan CUI Heju YANG Yuying QIAO College of Mathematics and Statistics Zhoukou Normal UniversityZhoukou 466001HenanChina College of Science Hebei University of Science and TechnologyShijiazhuang 050024China College of Mathematics and Information Science Hebei Normal UniversityShijiazhuang 050024China

In this paper,the authors extend the Roper-Suffridge operator on the generalized Hartogs *** mainly research the properties of the extended *** the characteristics of Hartogs domains and the geometric properties of subclasses of spirallike mappings,they obtain the extended Roper-Suffridge operator preserving almost starlikeness of complex orderλ,almost spirallikeness of typeβand orderα,parabolic spirallikeness of typeβand orderρon the Hartogs domains in different *** conclude that the corresponding extension operator preserves the same geometric invariance on the unit ball B^(n) in C^(n).The conclusions provide a new approach to study these geometric mappings in C^(n).

关键词： Roper-Suffridge operator spirallike mappings Starlike mappings

PROPERTIES OF THE MODIFIED ROPER-SUFFRIDGE EXTENSION OPERATORS ON REINHARDT DOMAINS

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Acta Mathematica Scientia 2016年第6期36卷 1767-1779页

作者：王朝君崔艳艳刘浩 College of Mathematics and Statistics Zhoukou Normal University College of Mathematics and Statistics Henan University

In this paper, we mainly discuss the properties of the modified Roper-Suffridge operators on Reinhardt domains. By the analytical characteristics and distortion results of subclasses of biholomorphic mappings, we conclude that the modified Roper-Suffridge operators preserve the properties of SΩ （β, A, B）, almost starlike mapping of complex order A on Ωn,p2……pn. Sequentially, we get that the modified Roper-Suffridge operators preserve spirallikeness of type β and order a, strongly pirallikeness of type β and order a, almost starlikeness of order a on Ωn,p2……pn The conclusions provide a new approach to construct these biholomorphic mappings which have special geometric properties in several complex variables.

关键词： Roper-Suffridge operator spirallike mappings starlike mappings