[1]林珍连.某些调和单叶函数的稳定性及系数估计[J].华侨大学学报(自然科学版),2009,30(6):718-719.[doi:10.11830/ISSN.1000-5013.2009.06.0718]
　LIN Zhen-lian.The Stability and Coefficient Estimates for Some Harmonic Univalent Mappings[J].Journal of Huaqiao University(Natural Science),2009,30(6):718-719.[doi:10.11830/ISSN.1000-5013.2009.06.0718]
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某些调和单叶函数的稳定性及系数估计()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第30卷
期数:
2009年第6期
页码:
718-719
栏目:
出版日期:
2009-11-20

文章信息/Info

Title:
The Stability and Coefficient Estimates for Some Harmonic Univalent Mappings
文章编号:
1000-5013(2009)06-0718-02
作者:
林珍连
华侨大学数学科学学院
Author(s):
LIN Zhen-lian
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
调和单叶函数;  线性连接区域;  稳定性;  系数估计
Keywords:
harmonic univalent function;  linearly connected domain;  stability;  coefficient estimate
分类号:
O174.55
DOI:
10.11830/ISSN.1000-5013.2009.06.0718
文献标志码:
A
摘要:
利用线性连接区域作为工具,研究单位圆盘上的复值调和函数f=h+g-,证明h+βeiθg及h+βeiθg-具有单叶性,其中0≤β≤1,θ∈R.据此,证明某些调和单叶映射在特定条件下的系数估计猜想||a0n|-|a0-n||≤n,n=2,3,…,是真的.
Abstract:
In this paper,the linearly connected domains are used as a tool to prove the functions h+βeiθg and h+βeiθg,0≤β≤1,θ∈R to be univalent for the harmonic complex function f=h+g in the unit disk.On this basis,the conjucture of coefficient estimates ||a0n|-|a0-n||≤n,n=2,3,…,for some harmonic univalent functions under specific conditions are proved to be correct.

参考文献/References:

[1] LEWY H. On the non-vanishing of the Jacobian in certain one-to-one mappings [J]. Bulletin of the American Mathematical Society, 1936, (10):689-692.doi:10.1090/S0002-9904-1936-06397-4.
[2] CLUNIE J, SHEIL-SNALL T. Harmonic univalent functions [J]. Annales Academiae Scientiarum Fennicae Series AI Mathematica, 1984(9):3-25.
[3] 吴瑞溢, 黄心中. 单叶调和函数的稳定性 [J]. 漳州师范学院学报(自然科学版), 2007(2):11-15.doi:10.3969/j.issn.1008-7826.2007.02.003.
[4] POMMERENKE C H, 杨维奇. 单叶函数 [M]. 北京:科学出版社, 1984.
[5] 黄心中. 给定复伸张单叶调和映照的面积偏差 [J]. 华侨大学学报(自然科学版), 2007(2):208-211.doi:10.3969/j.issn.1000-5013.2007.02.025.
[6] CHUAQUI M, HERNNDEZ R. Harmonic univalent mappings and linearly connected domain [J]. Journal of Mathematical Analysis and Applications, 2007(2):1189-1194.

备注/Memo

备注/Memo:
华侨大学科研基金资助项目(07HZR03,09HZR23)
更新日期/Last Update: 2014-03-23