螺形映照的新子族

数学物理学报 ›› 2015, Vol. 35 ›› Issue (4): 683-694.

螺形映照的新子族

王朝君¹, 崔艳艳¹, 刘浩², 朱思峰¹

1 周口师范学院数学与统计学院, 河南周口 466001;
2 河南大学数学与信息科学学院, 河南开封 475001

收稿日期:2014-06-11 修回日期:2015-01-29 出版日期:2015-08-25 发布日期:2015-08-25
通讯作者: 朱思峰, zhusifeng@163.com E-mail:zhusifeng@163.com
作者简介:王朝君, wang9907081@163.com
基金资助:
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

New Subclasses of Spirallike Mappings

Wang Chaojun¹, Cui Yanyan¹, Liu Hao², Zhu Sifeng¹

1 College of Mathematics and Statistics, Zhoukou NormalUniversity, Henan Zhoukou 466001;
2 College ofMathematics and Information Science, Henan University, Henan Kaifeng 475001

Received:2014-06-11 Revised:2015-01-29 Online:2015-08-25 Published:2015-08-25

摘要/Abstract

摘要：

定义了螺形函数的新子族, 即ρ次椭圆星形函数和ρ次椭圆形β型螺形函数,并将这些定义推广到多复变数空间中, 得到推广的Roper-Suffridge算子在不同空间不同区域上保持ρ次椭圆星形映照和ρ次椭圆形β型螺形映照的性质, 由此可以在多复变数空间中构造出许多ρ次椭圆形β型螺形映照. 所得结论丰富了对螺形映照子族及推广的Roper-Suffridge算子的研究.

关键词: Roper-Suffridge算子, 星形映照, 螺形映照, Reinhardt域

Abstract:

In this paper, we introduce some new subclasses of spirallike functions, namely elliptical starlike functions of order ρ, elliptical and spirallike functions of type β and order ρ. We extend the new definitions and obtain that the generalized Roper-Suffridge operators preserve the properties of the mappings defined in this paper on different domains in different spaces, thus many elliptical and spirallike mappings of type β and order ρ can be constructed in several complex variables. The conclusions enrich the research of subclasses of spirallike mappings and generalized Roper-Suffridge operators.

Key words: Roper-Suffridge operators, Starlike mappings, Spirallike mappings, Reinhardt domains

中图分类号:

O174.56

王朝君, 崔艳艳, 刘浩, 朱思峰. 螺形映照的新子族[J]. 数学物理学报, 2015, 35(4): 683-694.

Wang Chaojun, Cui Yanyan, Liu Hao, Zhu Sifeng. New Subclasses of Spirallike Mappings[J]. Acta mathematica scientia,Series A, 2015, 35(4): 683-694.

参考文献

[1] Cartan H. Sur la possibilite d'etendre aux fonctions de plusieurs variables complexes la theorie des fonctions univalents//Montel P. Lecons sur les Fonctions Univalents on Mutivalents. Paris: Gauthier-Villars, 1933: 129-155
[2] Rønning F. On starlike functions associated with parabolic regions. Ann Univ Mariae Curie Sklodowska, 1991, 45: 117-122
[3] Rønning F. Uniformly convex functions and a corresponding class of starlike functions. Proc Amer Math Soc, 1993, 118: 189-196
[4] Ali R M. Starlikeness associated with parabolic regions. Int J Math Sci, 2005, 44: 561-570
[5] Hamada H, Honda T, Kohr G. Parabolic starlike mappings in several complex variables. Manucscripta Math, 2007, 123: 301-324
[6] 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
[7] Roper K A, Suffridge T J. Convex mappings on the unit ball of Cⁿ. J Anal Math, 1995, 65: 333-347
[8] 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
[9] Feng S X, Liu T S. Uniformly starlike mappings and uniformly convex mappings on the unit ball Bn. Acta Math Sci, 2014, 34B(2): 435-443
[10] 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
[11] Wang J F. Modifiled Roper-Suffridge operator for some subclasses of starlike mappings on Reinhardt domains. Acta Math Sci, 2013, 33B(6): 1627-1638
[12] Chuaqui M. Applications of subordination chains to starlike mappings in Cn. Pacif J Math, 1995, 168: 33-48
[13] 崔艳艳, 王朝君. 复Banach空间上推广的Roper-Suffridge延拓算子. 数学杂志, 2014, 34(3): 515-520
[14] Liu T S, Zhang W J. On decomposition theorem of normalized biholomorphic convex mappings in Reinhardt domains. Science in China, 2003, 1: 94-106
[15] 刘名生, 朱玉灿. 有界完全Reinhardt域上推广的Roper-Suffridge算子. 中国科学(A), 2007, 37(10): 1193-1206
[16] 阮林要.Roper-Suffridge算子与Loewner链.开封:河南大学,2009