[1]王其文,黄心中.在微分算子作用下调和函数的单叶半径估计[J].华侨大学学报(自然科学版),2014,35(2):227-231.[doi:10.11830/ISSN.1000-5013.2014.02.0227]
　WANG Qi-wen,HUANG Xin-zhong.On the Estimates of Univalent Radius for Harmonic Mappings under the Differential Operator[J].Journal of Huaqiao University(Natural Science),2014,35(2):227-231.[doi:10.11830/ISSN.1000-5013.2014.02.0227]
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在微分算子作用下调和函数的单叶半径估计()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第35卷
期数:
2014年第2期
页码:
227-231
栏目:
出版日期:
2014-03-20

文章信息/Info

Title:
On the Estimates of Univalent Radius for Harmonic Mappings under the Differential Operator
文章编号:
1000-5013(2014)02-0227-05
作者:
王其文;  黄心中
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
WANG Qi-wen;  HUANG Xin-zhong
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
调和函数;  微分算子;  单叶半径;  系数估计
Keywords:
harmonic mapping;  differential operator;  univalent radius;  coefficient estimate
分类号:
O174.5
DOI:
10.11830/ISSN.1000-5013.2014.02.0227
文献标志码:
A
摘要:
基于单叶调和函数系数模估计的猜想, 在调和函数f(z)=h(z)+g(z)^-的系数模满足猜想条件下,研究 f(z)在L=z?/(?z)-(-overz)?/(?(-overz))作用下的单叶半径问题,分别得到精确的单叶半径表达式.结果表明:在系数模估计满足更一般表达式的条件下,同样也能得到在L作用下L(f)的精确单叶半径估计.
Abstract:
Let f(z)=h(z)+g(z)^- be a harmonic mapping on the unit disk D={z||z|<1}, L represents the differential operator L=z?/(?z)-(-overz)?/(?(-overz)). Under the coefficients satisfying two famous conjecture bounds for univalent harmonic functions on D, we obtain two sharp univalent radii for Lf(z)=z(?f)/(?z)-(-overz)(?(-overf))/(?(-overz)). Moreover, with the condition that the coefficients satisfying one general expression, we also obtain the similar sharp result.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期: 2012-10-17
通信作者: 黄心中(1957-),男,教授,主要从事函数论的研究.E-mail:huangxz@hqu.edu.cn.
基金项目: 福建省自然科学基金资助项目(2011J0101)
更新日期/Last Update: 2014-03-20