[1]王其文,黄心中.某些调和函数的系数估计与像区域的近于凸性质[J].华侨大学学报(自然科学版),2013,34(2):225-229.[doi:10.11830/ISSN.1000-5013.2013.02.0225]
　WANG Qi-wen,HUANG Xin-zhong.Coefficient Estimate and Close-to-Convex Image Domain Property for Some Harmonic Functions[J].Journal of Huaqiao University(Natural Science),2013,34(2):225-229.[doi:10.11830/ISSN.1000-5013.2013.02.0225]
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某些调和函数的系数估计与像区域的近于凸性质()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第34卷
期数:
2013年第2期
页码:
225-229
栏目:
出版日期:
2013-03-20

文章信息/Info

Title:
Coefficient Estimate and Close-to-Convex Image Domain Property for Some Harmonic Functions
文章编号:
1000-5013(2013)02-0225-05
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;  拟共形映照;  系数不等式;  近于凸
Keywords:
harmonic mapping;  quasiconformal mapping;  coefficient inequality;  close-to-convex
分类号:
O174.5
DOI:
10.11830/ISSN.1000-5013.2013.02.0225
文献标志码:
A
摘要:
研究定义在单位圆盘D={z||z|<1}上的调和函数类C2H(λ),得到C2H(λ)类中的函数为调和拟共形映照的一个充分条件,并给出调和函数的解析部分、共轭解析部分的系数估计.在调和映照系数模满足一定的条件下,给出该类函数的近于凸单叶半径与星像单叶半径估计,主要结果改进和推广了Kalaj等的相应结论.
Abstract:
Let C2H(λ)be the harmonic mappings on the unit disk D={z||z|<1}. In this paper, we first find one sufficient condition for them to be harmonic quasiconformal mappings and give their analytical part and conjugate part’s coefficient estimate. Next, under one coefficient bound condition for harmonic functions, we find the lower bound estimates for their close-to-convex and star-like radius in their image domains. Our results improve and generalize the one made by Kalaj recently.

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备注/Memo

备注/Memo:
收稿日期: 2012-05-29
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: 2013-03-20