[1]黄心中,黄赟.某类调和函数的单叶半径和Landau定理[J].华侨大学学报(自然科学版),2016,37(1):120-124.[doi:10.11830/ISSN.1000-5013.2016.01.0120]
　HUANG Xinzhong,HUANG Yun.On the Univalent Radius and Landau Theorem for Some Harmonic Mappings[J].Journal of Huaqiao University(Natural Science),2016,37(1):120-124.[doi:10.11830/ISSN.1000-5013.2016.01.0120]
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某类调和函数的单叶半径和Landau定理()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第37卷
期数:
2016年第1期
页码:
120-124
栏目:
出版日期:
2016-01-03

文章信息/Info

Title:
On the Univalent Radius and Landau Theorem for Some Harmonic Mappings
文章编号:
1000-5013(2016)01-0120-05
作者:
黄心中;  黄赟
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
HUANG Xinzhong;  HUANG Yun
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
调和函数;  稳定近于凸;  单叶半径;  Landau定理
Keywords:
harmonic mapping;  stable close-to-convex;  univalent radius;  Landau theorem
分类号:
O174.51;O174.55
DOI:
10.11830/ISSN.1000-5013.2016.01.0120
文献标志码:
A
摘要:
研究单位圆盘D上解析部分h(z)满足Re({1+z(h″(z))/(h’(z))}>c(-1/2<c≤0)的调和函数f(z)=h(z)+g(z)^-的单叶性问题,对其复伸张w(z)为zn及|w(z)|<1的情况,分别给出f(z)的稳定近于凸半径和单叶半径估计.并在同时满足其他条件的情况下,给出单叶区域在调和函数作用下值域最大覆盖圆半径的估计,推广了Chen等的结果.
Abstract:
To the harmonic mappings f(z)=h(z)+g(z)^- with their analytic parts h(z)have the property of Re({1+z(h″(z))/(h’(z))}>c(-1/2<c≤0)on a unit disk D, if the dilatation function w(z)=zn or |w(z)|<1, the stable close-to-convex radius and the univalent radius estimates are obtained respectively. Moreover, we also consider Landau theorem for harmonic functions with some other conditions, our results improve the one made by Chen.

参考文献/References:

[1] BSHOUTY D,LYZZAIK A.Close-to-convexity criteria for planar harmonic mappings [J].Complex Analysis and Operator Theory,2011,5(3):767-774.
[2] MOCANU P T.Injectivity conditions in the complex plane[J].Complex Anal Oper Theory,2011,5(3):759-766.
[3] BSHOUTY D,LYZZAIK A.Problems and conjectures in planar harmonic mappings[J].J Analysis,2010,18:69-81.
[4] 黄赟,黄心中.某些近于凸调和函数的解析性质和系数估计[J].华侨大学学报(自然科学版),2015,36(4):478-483.
[5] HERNáNDEZ R,MARTíN M T.Stable geometric properties of analytic and harmonic functions[J].Math Proc Camb Phil Soc,2013,155(2):343-359.
[6] 石擎天,黄心中.调和映照与其剪切函数的单叶性[J].华侨大学学报(自然科学版),2013,34(3):334-338.
[7] 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.
[8] CHEN Huaihui,GAUTHIER P M.The landau theorem and bloch theorem for planar harmonic and pluriharmonic mappings[J].Proceeding of the American Mathematical Society,2011,139(2):583-595.
[9] 李东征,陈行堤.调和函数的Landau定理[J].华侨大学学报(自然科学版),2012,33(5):584-289.
[10] 李东征,陈行堤.调和函数的Bloch定理[J].华侨大学学报(自然科学版),2012,33(1):103-106.

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备注/Memo

备注/Memo:
收稿日期: 2015-08-23
通信作者: 黄心中(1957-),男,教授,博士,主要从事函数论的研究.E-mail:huangxz@hqu.edu.cn.
基金项目: 国家自然科学基金资助项目(11471128); 福建省自然科学基金资助项目(2014J01013)
更新日期/Last Update: 2016-01-20