改进的Roper-Suffridge算子的性质及其偏差

Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (6): 1611-1618.

• Articles • Previous Articles Next Articles

The Property and the Distortion |of the Generalized Roper-Suffridge Extension Operators

CUI Yan-Yan¹, WANG Chao-Jun¹, LIU Hao², ZHU Sai-Feng^1*

1.College of Mathematics and Statistics, Zhoukou Normal University, Henan\quad Zhoukou 466001;
2.College of Mathematics and Information Science, Henan University, Kaifeng 475001

Received:2013-10-30 Revised:2014-08-29 Online:2014-12-25 Published:2014-12-25
Supported by:
国家自然科学基金(11271359, U1204618)、河南省自然科学基金(2011B110034)和河南省教育厅科学技术研究重点项目(14B110015, 14B110016)资助

Abstract

Abstract:

In this paper, the authors generalize the Roper-Suffridge extension operator, and discuss that the generalized operators preserve some properties of subclasses of biholomorphic mappings. From the definition, they prove the fact that the generalized operators preserve spirallikeness of type β and order α and strongly spirallikeness of type β, and as the special case, they obtain that the generalized operators preserve starllikeness of order α and strongly starllikeness on the corresponding domain, and they also research the distortion of the generalized operators.

Key words: Roper-Suffridge operators, Spirallike mappings of type &beta, and order α, Strongly spirallike mappings of type β, Distortion theorem

CLC Number:

32A30

CUI Yan-Yan, WANG Chao-Jun, LIU Hao, ZHU Sai-Feng. The Property and the Distortion |of the Generalized Roper-Suffridge Extension Operators[J].Acta mathematica scientia,Series A, 2014, 34(6): 1611-1618.

Trendmd

References

[1] Chuaqui M. Applications of subordination chains to starlike mappings in Cⁿ. Pacif J Math, 1995, 168(1): 33--48

[2] Kohr G, Liczberski P. On strongly starlikeness of order alpha in several complex variables. Glasnik Matem, 1995, 33(53): 185--198

[3] Graham I, Kohr G. Univalent mappings associated with the Roper-Suffridge extension operator. Analyse Math, 2000, 81(1): 331--342

[4] Liu M S, Zhu Y C. On the extension operator in Banach spaces. Advances in Math, 2005, 34(4): 506--508

[5] 刘小松, 刘太顺. Reinhardt域上和复Hilbert空间单位球上推广的Roper-Suffridge算子. 数学年刊, 2005, 26A(5): 721--730

[6] Feng S X, Liu T S. The generalized Roper-Suffridge extension operator. Acta Math Sci, 2008, 28B(1): 63--80

[7] 徐庆华, 刘太顺. 正规化双全纯映照的增长和掩盖定理. 数学年刊, 2009, 30A(2): 213--220

[8] 邹娟. 复Banach空间中的Roper-Suffridge算子. 数学物理学报, 2010, 30A(6): 1582--1591

[9] Liu X S, Feng S X. A remark on the generalized Roper-Suffridge extension operator for spirallike mappings of type
β and order α. Chin Quart J of Math, 2009, 24(2): 310--316

[10] 冯淑霞, 张晓飞, 陈慧勇. 多复变数的抛物星形映射. 数学学报, 2011, 54(3): 467--482

[11] Muir J R. A modification of the Roper-Suffridge extension operator. Comput Methods Funct Theory, 2005, 5(1): 237--251

[12] Muir J R, Suffridge T J. Unbounded convex mappings of the ball in Cⁿ. Trans Amer Math Soc, 2001, 129(11): 3389--3393

[13] Muir J R, Suffridge T J. Extreme points for convex mappings of Bⁿ. J Anal Math, 2006, 98: 169--182

[14] Kohr G. Loewner chains and a modification of the Roper-Suffridge extension operator. Mathematica, 2006, 71(1): 41--48

[15] Muir J R. A class of Loewner chain preserving extension operators. J Math Anal Appl, 2008, 337(2): 862--879

[16] 王建飞, 刘太顺. 全纯映照子族上改进的Roper-Suffridge算子. 数学年刊, 2010, 31A(4): 487--496

[17] 冯淑霞.多复变函数的几类全纯映射族. 合肥: 中国科学技术大学, 2004

[18] Koebe P. "{U}ber die Uniformisierung beliebiger analylischer kurven. Nachr Akad Wiss G\"{o}ttingen, Math Phys Kl, 1907, 1907(1): 191--210

[19] Hamada H, Kohr G. The growth theorem and quasiconformal extension of strongly spirallike mappings of type β.
Complex variables, 2001, 44(4): 281--297

The Property and the Distortion |of the Generalized Roper-Suffridge Extension Operators

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 2

Metrics

Comments

Recommended 10

[1]	Wang Chaojun, Cui Yanyan, Liu Hao. Generalized Roper-Suffridge Extension Operators and Loewner Chains [J]. Acta mathematica scientia,Series A, 2016, 36(3): 433-440.
[2]	Wang Chaojun, Cui Yanyan, Liu Hao, Zhu Sifeng. New Subclasses of Spirallike Mappings [J]. Acta mathematica scientia,Series A, 2015, 35(4): 683-694.