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Estimates on Bloch constants for planar harmonic mappings 被引量：16

Estimates on Bloch constants for planar harmonic mappings
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摘要 The Bloch constants for quasiregular harmonic mappings and open planar harmonic mappings are considered. Better estimates are obtained. The results, presented in this paper, improve the one made by Chen et al. and Grigoryan. The Bloch constants for quasiregular harmonic mappings and open planar harmonic mappings are considered. Better estimates are obtained. The results, presented in this paper, improve the one made by Chen et al. and Grigoryan.
作者 LIU MingSheng School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
出处 《Science China Mathematics》 SCIE 2009年第1期87-93,共7页 中国科学：数学（英文版）
基金 supported by the Research Foundation for Doctor Programme (Grant No. 20050574002) the National Natural Science Foundation of China (Grant No. 10471048)
关键词 Bloch constant quasiregular harmonic mapping open planar harmonic mapping 30C99 30C62 Bloch constant quasiregular harmonic mapping open planar harmonic mapping
分类号 O174.3 [理学—基础数学]
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参考文献10

  • 1Huaihui Chen,Chengji Xiong.Julia’s lemma and bloch constants[J]. Science in China Series A: Mathematics . 2003 (3)
  • 2DorM,Nowak M.Landau’s theorem for planar harmonic mappings. Comput Methods Funct Theory . 2000
  • 3Grigoryan A.Landau and Bloch theorems for harmonic mappings. Complex Variables Theory and Application . 2006
  • 4Huang X Z.Estimates on Bloch constants for planar harmonic mappings. Journal of Mathematical Analysis and Applications . 2007
  • 5Chen H H,Xiong C J.Julia’s lemma and Bloch constants. Sci China Ser A-Math . 2003
  • 6Chen H H.On the Bloch constant. Approximation, Complex Analysis, and Potential Theory . 2001
  • 7Lewy,H.On the non-vanishing of the Jacobian in certain one-to-one mappings. Bulletin of the American Mathematical Society . 1936
  • 8CHEN H,,GAUTHIER P M,HENGARTNER W.Bloch constants for planar harmonic mappings. Poc AmerMath Soc . 2000
  • 9Graham,I.,Kohr,G. Geometric Function Theory in One and Higher Dimensions . 2003
  • 10Kuang Jichang.Applied Inequalities. . 2004

同被引文献60

  • 1龙波涌,黄心中.Beurling-Ahlfors延拓的伸张函数[J].数学杂志,2006,26(4):446-450. 被引量：3
  • 2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. 被引量：6
  • 3DUREB P.Harmonic mappings in the plane[M].Cabridge:Cabridge Univ Press,2004.
  • 4ABDULHADI Z,MUHANNA Y A.Landau's theorem for biharmonic mappings[J].J Math Anal Appl,2008,338(1):705-709.
  • 5CHEN S.PONNUSAMY S,WANG X.Landau's theorem for certain biharmonic mappings[J].Applied Mathematics and Computation,2009,208 (2):427-433.
  • 6LEWY H.On the non-vanishing of the Jacobian in certain one-to-one mappings[J].Bull Amer Math Soc,1936,42(10):689-692.
  • 7CHEN H H,GAUTHIER P M,HENGARTNER W.Bloch constants for planar harmonic mappings[J].Proc Amer Math Soc,2000,128 (11):3231-3240.
  • 8HUANG Xin-zhong.Estimates on Bloch constants for planar harmonic mappings[J].J Math Anal Appl,2007,337(2):880-887.
  • 9LIU Ming-sheng.Landau's theorem for planar harmonic mappings[J].Computers and Mathematics with Appications,2009,57(7):1142-1146.
  • 10LIU Ming-sheng.Landau's theorems for biharmonic mappings[J].Comlex Variables and Elliptic Equations,2008,53(9):843-855.

引证文献16

二级引证文献25

Science China Mathematics
2009年 第1期

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