复Banach空间中的Roper-Suffridge算子

数学物理学报 ›› 2010, Vol. 30 ›› Issue (6): 1582-1591.

复Banach空间中的Roper-Suffridge算子

邹娟

收稿日期:2008-01-18 修回日期:2009-10-11 出版日期:2010-12-25 发布日期:2010-12-25
基金资助:
国家自然科学基金(10571121)和广东省自然科学基金(5010509)资助

The Roper-Suffridge Extension Operator in Complex Banach Space

ZU Juan

College of Mathematics and Computational Science, Shenzhen University, Guangdong Shenzhen 518060

Received:2008-01-18 Revised:2009-10-11 Online:2010-12-25 Published:2010-12-25
Supported by:
国家自然科学基金(10571121)和广东省自然科学基金(5010509)资助

摘要/Abstract

摘要：

该文将Roper-Suffridge算子推广到一般的复Banach空间中, 并证明了其在相应域上保持α 型螺形性, 而另一种推广形式的Roper-Suffridge算子在复Banach空间中的单位球上保持α次星形性. 因而将刘太顺、刘小松和冯淑霞等学者在Hilbert空间中的一些结果推广到了Banach空间.

关键词: Roper-Suffridge算子, &alpha, 型螺形性, α次星形性, 复Banach空间

Abstract:

In this paper, the author extends the Roper-Suffridge operator to some domains in complex Banach space, and it is proved that certain extended Roper-Suffridge operator preserves spirallikeness of type α on the relevant domain, while another extended Roper-Suffridge operator preserves starlikeness of order α on the unit ball in a complex Banach space. Some results of Liu T S , Liu X S and Feng S X in Hilbert space are extended to Banach spaces.

Key words: Roper-Suffridge operator, Spirallike mapping of type α, Starlike mapping of order α, Complex Banach space

中图分类号:

32A30

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

ZU Juan. The Roper-Suffridge Extension Operator in Complex Banach Space[J]. Acta mathematica scientia,Series A, 2010, 30(6): 1582-1591.

[1]	夏红川, 刘浩, 钟春平. 复Hilbert空间单位球上一类新的Roper-Suffridge算子[J]. 数学物理学报, 2017, 37(4): 637-646.
[2]	王朝君, 崔艳艳, 刘浩. Roper-Suffridge延拓算子与Loewner链[J]. 数学物理学报, 2016, 36(3): 433-440.
[3]	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.
[4]	崔艳艳, 王朝君, 刘浩, 朱思峰. 改进的Roper-Suffridge算子的性质及其偏差[J]. 数学物理学报, 2014, 34(6): 1611-1618.
[5]	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, 29(6): 1601-1612.
[6]	冯淑霞; 刘太顺. α次的殆星映射的充分判别条件[J]. 数学物理学报, 2007, 27(3): 506-514.