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复合解析函数族分担亚纯函数的正规性 被引量:2

Nomal families of composite analytic functions and sharing a meromorphic function
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摘要 本文推广了Bergweiler的一个正规定则:设α(z)和F分别是区域D上的非常数解析函数与解析函数族,R(z)是一个次数不低于2的有理函数.如果对族F中函数f(z)和g(z),Rof(z)和Rog(z)分担α(z)IM,并且下述条件之一成立:(1)对任意z0∈D,R(z)-α(z0)有至少两个不同的零点或极点;(2)存在z0∈D使得R(z)-α(z0):=P(z)Q(z)仅有一个零点(或极点)β0,同时k=lp(或k=lq),其中l和k分别是f(z)-β0和α(z)-α(z0)在z0处的零点重数,P(z)和Q(z)分别是次数为p和q的互质的多项式,并且α(z0)∈C∪{∞}.那么F在D内正规. A result of Bergweiler is extended and an alternative proof is given in this paper.Our main result is as follows:Letα(z)be a nonconstant meromorphic function,F be a family of analytic functions in a domain D,and R(z)be a rational function of degree at least 2.If Rof(z)and Rog(z)shareα(z)IM for each pair f(z),g(z)∈F and one of the following conditions holds: (1)R(z)-α(z0)has at least two distinct zeros or poles for any z0∈D; (2)There exists z0∈D such that R(z)-α(z0):= P(z) /Q(z) has only one distinct zero(or pole)β0 and suppose that the multiplicities l and k of zeros of f(z)-β0 andα(z)-α(z0)at z0,respectively,satisfy k≠lp(or k≠lq),possibly outside finite f(z)∈F,where P(z)and Q(z)are two of no common zero polynomials with degree p and q respectively,andα(z0)∈C∪{∞}. Then F is normal in D. Some examples are given to illustrate that the conditions in above result are necessary.
出处 《中国科学:数学》 CSCD 北大核心 2010年第5期429-436,共8页 Scientia Sinica:Mathematica
基金 国家自然科学基金(批准号:10771220) 教育部博士点基金(批准号:200810780002)资助项目
关键词 复合函数 正规定则 分担值 meromorphic function normal family rational function share value
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参考文献12

  • 1Yang L. Value Distribution Theory. Berlin: Springer-Verlag, 1993.
  • 2Rosenbloom P C. The fix-points of entire functions. Medd Lunds Univ Mat Sem, 1952, Suppl: 186-192.
  • 3Hayman W K. Meromorphic Functions. Oxford: Clarendon Press, 1964.
  • 4Bergweiler W. Bloch's principle. Comput Methods Funct Theory, 2006, 6:77-108.
  • 5Fang M L, Yuan W J. On the normality for families of meromorphic functions. Indian J Math, 2001, 43:341 -351.
  • 6Zheng J H, Yang C C. Further results on fixpoints and zeros of entire functions. Trans Amer Math Soc, 1995, 347: 37-50.
  • 7Fang M L, Yuan W J. On Rosenbloom's fix-points theorem and related results. J Austral Math Soc Ser A, 2000, 68: 321-333.
  • 8Bergweiler W. Fixed points of composite meromorphic functions and normal families. Proc Royal Soc Edinburgh Sec A Math, 2004, 134:653-660.
  • 9Yuan W J, Li Z R, Xiao B. A normal criterion of composite analytic functions and sharing an analytic function. J Guangzhou Univ, in press.
  • 10Zalcman L. A heuristic principle in complex function theory. Amer Math Monthly, 1975, 82:813-817.

同被引文献17

  • 1LEI ChunLin 1 & FANG MingLiang 2, 1 Department of Applied Mathematics, South China Agricultural University, Guangzhou 510642, China,2 Institute of Applied Mathematics, South China Agricultural University, Guangzhou 510642, China.Normality and shared values concerning differential polynomials[J].Science China Mathematics,2010,53(3):749-754. 被引量:8
  • 2陈怀惠,方明亮.关于f^nf'的值分布[J].中国科学(A辑),1995,25(2):121-127. 被引量:39
  • 3Hayman W K. Meromorphic Fnctions. Oxford: Clarendon Press, 1964.
  • 4Yang L. Value Distribution Theory. Berlin: Springer-Verlag, 1993.
  • 5Chang J M, Fang M L, Zalcman L. Composite meromorphic functions and normal families. Proc Royal Society Edinburgh, 2009, 139:57-72.
  • 6Fang M L, Yuan W J. On Rosenbloom's fix-points theorem and related results. J Austral Math Soc Ser A, 2000, 68: 321-333.
  • 7Bergweiler W. Fixed points of composite meromorphic functions and normal families. Proc Royal Soc Edinburgh Sect A Math, 2004, 134:653-660.
  • 8Hinchliffe J D. Normality and fixpoints of holomorphic functions. Proc Royal Society Edinburgh. Sect A-Mathematical and Physical Sciences, 2003, 133:1335-1339.
  • 9Yuan W J, Xiao B, Wu Q F. Composite meromorphic functions and normal families. Arch Math, 2011, 96:435-444.
  • 10Fang M L, Hong W. Some results on normal family of meromorphic functions. Bull Amer Math Soc (Second Series), 2000, 23:143-151.

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