[1]朱剑峰,王朝祥,黄心中.单位圆上调和映照的单叶半径[J].华侨大学学报(自然科学版),2012,33(5):581-583.[doi:10.11830/ISSN.1000-5013.2012.05.0581]
　ZHU Jian-feng,WANG Chao-xiang,HUANG Xin-zhong.Univalent Radius of Harmonic Mapping in the Unit Disk[J].Journal of Huaqiao University(Natural Science),2012,33(5):581-583.[doi:10.11830/ISSN.1000-5013.2012.05.0581]
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单位圆上调和映照的单叶半径()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第33卷
期数:
2012年第5期
页码:
581-583
栏目:
出版日期:
2012-09-20

文章信息/Info

Title:
Univalent Radius of Harmonic Mapping in the Unit Disk
文章编号:
1000-5013(2012)05-0581-03
作者:
朱剑峰;  王朝祥;  黄心中
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
ZHU Jian-feng;  WANG Chao-xiang;  HUANG Xin-zhong
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
调和映照;  单叶半径;  星像函数;  凸像函数
Keywords:
harmonic mapping;  univalent radius;  starlike mapping;  convexity mapping
分类号:
O174.2
DOI:
10.11830/ISSN.1000-5013.2012.05.0581
文献标志码:
A
摘要:
设f(z)=h(z)+g(z)^-=z+∑+∞n=2anzn+∑+∞n=1bnzn^-为定义在单位圆盘U上的调和映照,满足条件∑+∞n=2np(|an|+|bn|)≤1-|b1|,证明当0&lt
Abstract:
Let f(z)=h(z)+g(z)^-=z+∑+∞n=2anzn+∑+∞n=1bnzn^- be a harmonic mapping of the unit disk U, satisfying ∑+∞n=2np×(|an|+|bn|)≤1-|b1|.In this paper we prove that: if 0<p≤1, then f(z)is univalent in the disk |z|<r0=1/(21-p); if 1<p≤2, then f(z)is convex in the disk |z|<R0=1/(22-p). These improve the corresponding results made by M. Jahangiri and M. Öztürk.

参考文献/References:

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[2] AHUJA P.Planar harmonic univalent and related mappings[J].Journal of Inequalitities in Pure and Applied Mathematics,2005,6(4):1-18.
[3] JAHANGIRI M,SILVERMAN H.Harmonic close-to-convex mappings[J].Journal of Applied Mathematics and Stochastic Analysis,2002,15(1):23-28.
[4] JAHANGIRI M,SILVERMAN H. Meromorphic univalent harmonic functions with negative coefficients[J].Bull Korean Math Soc,1999,36(4):763-770.
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[6] WIDOMAKI J,GREGORCZYK M.Harmonic mappings in the exterior of the unit disk[J].Annales UMCS, Mathematica,2010,64(1):63-73.

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备注/Memo

备注/Memo:
收稿日期: 2011-10-12
通信作者: 朱剑峰(1980-),男,讲师,主要从事函数论的研究.E-mail:flandy@hqu.edu.cn.
基金项目: 国家自然科学基金资助项目(11101165); 国务院侨办科研基金资助项目(10QZR22)
更新日期/Last Update: 2012-09-20