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Acta Mathematica Scientia 2016年第6期36卷 1804-1818页

作者：刘小松刘太顺 School of Mathematics and Computational Science Lingnan Normal University Zhanjiang 524048 China Department of Mathematics Huzhou University Huzhou 313000 China

In this article, first, the sharp estimates of all homogeneous expansions for a subclass of quasi-convex mappings of type B and order B on the unit ball in complex Ba- nach spaces are given. Second, the sharp estimates of all homogeneous expansions for the above generalized mappings on the unit polydisk in （in are also established. In particular, the sharp estimates of all homogeneous expansions for a subclass of quasi-convex mappings （include quasi-convex mappings of type A and quasi-convex mappings of type B） in several complex variables are get accordingly. Our results state that a weak version of the Bieber- bach conjecture for quasi-convex mappings of type B and order a in several complex variables is proved, and the derived conclusions are the generalization of the classical results in one complex variable.

关键词： homogeneous expansion quasi-convex mapping of type B and order a quasi-convex mapping quasi-convex mapping of type A quasi-convex mapping oftype B

The Estimates of All homogeneous expansions for a Subclass of ε Quasi-convex Mappings in Several Complex Variables

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Chinese Annals of Mathematics,Series B 2018年第4期39卷 621-632页

作者： Xiaosong LIU Taishun LIU School of Mathematics and Statistics Lingnan Normal University Zhanjiang 524048 Guangdong China. Department of Mathematics Huzhou Teachers College Huzhou 313000 Zhejiang China.

The authors obtain the estimates of all homogeneous expansions for a subclass of ε quasi-convex mappings on the unit ball in complex Banach spaces. Moreover, the estimates of all homogeneous expansions for the above generalized mappings on the unit polydisk in Cnare also obtained. Especially, the above estimates are only sharp for a subclass of starlike mappings, quasi-convex mappings and quasi-convex mappings of type A. The results are the generalization of many known results.

关键词： homogeneous expansion ε quasi-convex mapping ε starlike mapping Starlike mapping Quasi-convex mapping Quasi-convex mappings of type A

THE INVARIANCE OF STRONG AND ALMOST SPIRALLIKE MAPPINGS OF TYPE β AND ORDER α

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Acta Mathematica Scientia 2015年第6期35卷 1454-1466页

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

The invariance of strong and almost spirallike mappings of type β and order α is discussed in this paper. From the maximum modulus principle of holomorphic functions, we obtain that the generalized Roper-Suffridge operators preserve strong and almost spirallike-hess of type β and order α on the unit ball B^n in C^n and on bounded and complete Reinhardt domains. Therefore we obtain that the generalized Roper-Suffridge operators preserve strong spirllikeness of type β, strong and almost starlikeness of order α, strong starlikeness on the corresponding *** we can construct more subclasses of spirallike mappings in several complex variables.

关键词： strong and almost spirallike mappings of type β and order a Roper-Suffridgeoperators homogeneous expansion

A proof of a weak version of the Bieberbach conjecture in several complex variables

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Science China Mathematics 2015年第12期58卷 2531-2540页

作者： LIU XiaoSong LIU TaiShun XU QingHua School of Mathematics and Computation Science Lingnan Normal University Department of Mathematics Huzhou Teachers College College of Mathematics and Information Science Jiangxi Normal University

In this paper, the sharp estimates of all homogeneous expansions for a subclass of starlike mappings on the unit ball in complex Banach spaces are first established. Meanwhile, the sharp estimates of all homogeneous expansions for the above generalized mappings on the unit polydisk in Cnare also obtained. Our results show that a weak version of the Bieberbach conjecture in several complex variables is proved, and the obtained conclusions reduce to the classical results in one complex variable.

关键词： Bieberbach conjecture homogeneous expansion k-fold symmetric mapping a zero of order k + 1 starlike mapping

On the Second-order Item Coefficients for ε-starlike Mappings in C^n

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Chinese Quarterly Journal of Mathematics 2002年第4期17卷 78-82页

作者：尹清杰罗萍河南工业职业技术学院基础部河南南阳473009

Let B n be the unit ball in C n, we study ε-starlike mappings on B n. The upper bounds of second order item coefficients of homogeneous expansion for ε-starlike mappings are obtained.

关键词： starlike mappings homogeneous expansion