[1]王朝君,崔艳艳.有界完全Reinhardt域上的星形映照[J].四川师范大学学报(自然科学版),2018,(03):357-360.[doi:10.3969/j.issn.1001-8395.2018.03.014]
 WANG Chaojun,CUI Yanyan.Starlike Mappings on Bounded Complete Reinhardt Domains[J].Journal of SichuanNormal University,2018,(03):357-360.[doi:10.3969/j.issn.1001-8395.2018.03.014]
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有界完全Reinhardt域上的星形映照()
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2018年03期
页码:
357-360
栏目:
基础理论
出版日期:
2018-03-15

文章信息/Info

Title:
Starlike Mappings on Bounded Complete Reinhardt Domains
文章编号:
1001-8395(2018)03-0357-04
作者:
王朝君 崔艳艳
周口师范学院 数学与统计学院, 河南 周口 466001
Author(s):
WANG Chaojun CUI Yanyan
Deparment of Mathematics, Zhoukou Normal College, Zhoukou 466001, Henan
关键词:
Reinhardt域 星形映照 Roper-Suffridge算子
Keywords:
Reinhardt domains starlike mappings Roper-Suffridge operator
分类号:
O174.56
DOI:
10.3969/j.issn.1001-8395.2018.03.014
文献标志码:
A
摘要:
将Roper-Suffridge算子在Reinhardt 域上进行了推广,应用推广后的Roper-Suffridge延拓算子通过单位圆盘上全纯函数的α次凸性及近于凸性讨论多复变函数空间中相应的双全纯映照的星形性,从而得到Roper-Suffridge算子及其推广的新性质,并讨论算子的偏差.
Abstract:
In this paper, we generalize the Roper-Suffridge extension operators on Reinhardt domains. By applying the generalized opeator, we discuss the starlikeness of biholomorphic mappings by the convexity of order d close-to-convexity of holomorphic mappings on the unit disc, and then we obtain the new properties of the Roper-Suffridge extension operator. At last, we discuss the distortion of the generalized opeators.

参考文献/References:

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[2] ROPER K A, SUFFRIDGE T J. Convex mappings on the unit ball of Cn[J]. J Anal Math,1995,65:333-347.
[3] 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[J]. 数学年刊,2005,A26(5):721-730.
[4] FENG S X, LIU T S. Uniformly starlike mappings and uniformly convex mappings on the unit ball Bn[J]. Acta Math Sci,2014,B34(2):435-443.
[5] 崔艳艳,王朝君. 特定域上推广的Roper-Suffridge算子的性质[J]. 四川师范大学学报(自然科学版),2013,36(5):726-729.
[6] 冯淑霞,刘小松,徐庆华. Loewner链与推广的Roper-Suffridge算子[J]. 数学物理学报,2009,A29(6):1601-1612.
[7] ZHU Y C, LIU M S. Loewner chains associated with the generalized Roper-Suffridge extension operator on some domains[J]. J Math Anal Appl,2008,337:949-961.
[8] 王建飞,刘太顺. 全纯映射子族上改进的Roper-Suffridge算子[J]. 数学年刊,2010,31A(4):487-496.
[9] LIU H, XIA H C. A new Roper-Suffridge extension operator on bounded complete Reinhardt domains[J]. Acta Mathematica Scientia,2014,34B(6):1835-1844.
[10] GRAHAM I, KOHR G. Geometric Function Theory in One and Higher Dimensions[M]. New York:Marcel Dekker,2003.
[11] 刘名生,朱玉灿. 有界完全Reinhardt域上推广的Roper-Suffridge算子[J]. 中国科学,2007,A37(10):1193-1206. 〖=BTY(〗Starlike Mappings on Bounded Complete Reinhardt DomainsWANG Chaojun, CUI Yanyan(Deparment of Mathematics, Zhoukou Normal College, Zhoukou 466001, Henan)In this paper, we generalize the Roper-Suffridge extension operators on Reinhardt domains. By applying the generalized opeator, we discuss the starlikeness of biholomorphic mappings by the convexity of order α[J]. Acta Math Sci,2014,B34(2):435-443.
[5] 崔艳艳,王朝君. 特定域上推广的Roper-Suffridge算子的性质[J]. 四川师范大学学报(自然科学版),2013,36(5):726-729.
[6] 冯淑霞,刘小松,徐庆华. Loewner链与推广的Roper-Suffridge算子[J]. 数学物理学报,2009,A29(6):1601-1612.
[7] ZHU Y C, LIU M S. Loewner chains associated with the generalized Roper-Suffridge extension operator on some domains[J]. J Math Anal Appl,2008,337:949-961.
[8] 王建飞,刘太顺. 全纯映射子族上改进的Roper-Suffridge算子[J]. 数学年刊,2010,31A(4):487-496.
[9] LIU H, XIA H C. A new Roper-Suffridge extension operator on bounded complete Reinhardt domains[J]. Acta Mathematica Scientia,2014,34B(6):1835-1844.
[10] GRAHAM I, KOHR G. Geometric Function Theory in One and Higher Dimensions[M]. New York:Marcel Dekker,2003.
[11] 刘名生,朱玉灿. 有界完全Reinhardt域上推广的Roper-Suffridge算子[J]. 中国科学,2007,A37(10):1193-1206.

相似文献/References:

[1]王朝君,刘爱超,崔艳艳,等.Bn上螺形映照的子族与推广的Roper-Suffridge算子[J].四川师范大学学报(自然科学版),2016,(02):231.[doi:10.3969/j.issn.1001-8395.2016.02.014]
 WANG Chaojun,LIU Aichao,CUI Yanyan,et al.Subclasses of Spiral-like Mappings on Bn and the Generalized Roper-Suffridge Extension Operators[J].Journal of SichuanNormal University,2016,(03):231.[doi:10.3969/j.issn.1001-8395.2016.02.014]

备注/Memo

备注/Memo:
收稿日期:2016-11-11 接受日期:2017-03-04
基金项目:国家自然科学基金(11271359)和河南省教育厅科学技术研究重点项目(17A110041)
第一作者简介:王朝君(1981—),男,讲师,主要从事多复变函数论的研究,E-mail:wang9907081@163.com
更新日期/Last Update: 2018-03-15