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关于平面调和映射的Bloch常数的估计 被引量:1

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摘要 考虑了拟正则调和映射和开的平面调和映射的Bloch常数,得到了较好的结果,所得结果推广了陈怀惠等及Grigoryan的结果.
作者 刘名生
出处 《中国科学(A辑)》 CSCD 北大核心 2008年第8期851-858,共8页 Science in China(Series A)
基金 国家自然科学基金(批准号:10471048) 高等学校博士点基金(批准号:20050574002)资助项目
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参考文献10

  • 1Lewy H. On the non-vanishing of the Jacobian in certain one-to-one mappings. Bull Amer Math Soc, 42: 689-692 (1936).
  • 2Chen H H. On the Bloch constant. In: Arakelian N, Gauthier P M, eds. Approximation, Complex Analysis, and Potential Theory. Dordrecht: KLuwer Acad Publ, 2001, 129-161.
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  • 4Chen H H, Gauthier P M, Hengartner W. Bloch constants for planar harmonic mappings. Proc Amer Math Soc, 128:3231-3240 (2000).
  • 5Graham I, Kohr G. Geometric Function Theory in One and Higher Dimensions. New York: Marcel Dekker Inc, 2003.
  • 6Dorff M, Nowak M. Landau's theorem for planar harmonic mappings. Comput Meth Funet Theory, 4(1): 151-158 (2000).
  • 7Grigoryan A. Landau and Bloch theorems for harmonic mappings. Complex Variable Theory Appl, 51(1): 81-87 (2006).
  • 8Huang X Z. Estimates on Bloch constants for planar harmonic mappings. J Math Anal Appl, 337:880-887 (2007).
  • 9熊成继,陈怀惠.Julia引理和Bloch常数[J].中国科学(A辑),2002,32(9):791-796. 被引量:1
  • 10Kuang J C. Applied Inequalities, 3nd ed. Jinan: Shandong Science and Technology Press, 2004.

二级参考文献11

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同被引文献13

  • 1Chen H H, Gauthier P M, Hengartner W. Bloch constants for planar harmonic mappings. Proc Amer Math Soc, 2000 128:3231-3240.
  • 2Dorff M, Nowak M. Landau's theorem for planar harmonic mappings. Comput Methods Funct Theory, 2004, 4 151-158.
  • 3Grigoryan A. Landau and Bloch theorems for harmonic mappings. Complex Var Elliptic Equ, 2006, 51:81-87.
  • 4Huang X Z. Estimates on Bloch constants for planar harmonic mappings. J Math Anal Appl, 2007, 337:880-887.
  • 5Abdulhadi Z, Muhanna Y, Khuri S. On univalent solutions of the biharmonic equations. J Inequal Appl, 2005, 5 469-478.
  • 6Abdulhadi Z, Muhanna Y, Khuri S. On some properties of solutions of the biharmonic equation. Appl Math Comput 2006, 177:346-351.
  • 7Abdulhadi Z, Muhanna Y. Landau's theorem for biharmonic mappings. J Math Anal Appl, 2008, 338:705-709.
  • 8Liu M S, Liu Z W. On Bloch constants for certain harmonic mappings. Southeast Asian Bull Math, 2013, 37:211-220.
  • 9Liu M S. Landau's theorems for biharmonic mappings. Complex Var Elliptic Equ, 2008, 53:843-855.
  • 10Liu M S. Landau's theorems for planar harmonic mappings. Comput Math Appl, 2009, 57:1142-1146.

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