[1]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),2007,28(2):208-211.[doi:10.3969/j.issn.1000-5013.2007.02.025]
　HUANG Xin-zhong.Area Distortion for Univalent Harmonic Mappings with Given Dilatation[J].Journal of Huaqiao University(Natural Science),2007,28(2):208-211.[doi:10.3969/j.issn.1000-5013.2007.02.025]
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给定复伸张单叶调和映照的面积偏差()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第28卷
期数:
2007年第2期
页码:
208-211
栏目:
出版日期:
2007-04-20

文章信息/Info

Title:
Area Distortion for Univalent Harmonic Mappings with Given Dilatation
文章编号:
1000-5013(2007)02-0208-04
作者:
黄心中
华侨大学数学系 福建泉州362021
Author(s):
HUANG Xin-zhong
Department of Mathematics, Huaqiao University, Quanzhou 362021, China
关键词:
单叶调和映照;  复伸张;  面积偏差;  衰退性质
Keywords:
univalent harmonic mappings;  dilatation;  area distortion;  collapsing property
分类号:
O174.51
DOI:
10.3969/j.issn.1000-5013.2007.02.025
文献标志码:
A
摘要:
研究单位圆到自身内给定复伸张函数的单叶调和映照的面积偏差性质,得到精确的像区域面积上下限估计表达式,改进了由Hengartner和Schober得到的相应结果.
Abstract:
In this paper,area distortion properties for univalent harmonic mappings from open unit disk into itself with given dilatation is considered.Sharp forms of upper and lower bound for the image area are obtained.Our results improve the one made by Hengartner and Schober.

参考文献/References:

[1] HENGARTNER W, SCHOBER G. Harmonic mappings with given dilatation [J]. Journal of the London Mathematical Society, 1986(2):473-483.doi:10.1112/jlms/s2-33.3.473.
[2] CLUNIE J, SHEILSMALL T. Harmonic univalent functions [J]. Ann Acad Sci Fenn Ser, 1984(9):3-25.
[3] HALL R R. On an inequality of E.Heinz [J]. J Analyse Math, 1983.185-198.doi:10.1007/BF02786878.
[4] HENGARTNER W, SCHOBER G. Univalent harmonic functions [J]. Transactions of the American Mathematical Socity, 1987(1):1-31.
[5] DUREN P. Harmonic mappings in the plane [M]. London:Cambridge University Press, 2004.57-135.

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备注/Memo

备注/Memo:
福建省自然科学基金资助项目(Z0511025)
更新日期/Last Update: 2014-03-23