Meromorphic Functions Sharing Two Values

By using the idea of weighted sharing of values, the problem of uniqueness of meromorphic functions that share two values is studied. The results in this paper improve some theorems given by M. Ozawa and Yi Hongxun et al.     

具有亏值的亚纯函数的唯一性

改进了Ozawa的一个关于整函数的唯一性定理,得到了∞为亏值的亚纯函数唯一性的相应的几个结论.设亚纯函数f(z)与g(z)的级(或者下级)为有穷的非整数,满足.f=0→g=0,f=1g=1,f=∞9=∞,若∞为f(z)的Borel例外值,则f≡g.以及设f(z)与g(z)为C中非常数的亚纯函数,它们的级λ为有穷且非整数,再设它们满足f=0→g=0,f=1g=1,f=∞g=∞,若δ(∞,f)=1,f(z)为正规增长函数,则f≡g.     

具有公共值集和亏值的亚纯函数唯一性

§ 1 .　IntroductionandtheMainResult　　Inthispaper,weshallusethestandardnotationsofvaluesdistributiontheory(see [1]) .LetfbeameromorphicfunctionandSbeasetofdistinctelements.SetEf(S) =∪a∈S{z:f =a ,countingmultiplicities} .Recently,manygoodresultswereobtained(see [1— 4]) ,whichansweredthequestionofGross(see [5 ]) .TheoremA(see [3])　LetS1 ={ 0 } ,S2 ={z :z2 (z+a) -b =0 } ,wherea,baretwononzeroconstantssuchthatthealgebraicequationz2 (z+a) -b=0hasnomultipleroots.Iff ,garetwoentirefunctio…     

Shared Values of Certain Nonlinear Differential Polynomials of Meromorphic Functions

In this paper,by using the idea of truncated counting functions of meromorphic functions,we deal with the problem of uniqueness of the meromorphic functions whose certain nonlinear differential polynomials share one finite nonzero value.     

具有亏值的亚纯函数的唯一性定理

本文主要就具有某些特殊亏值关系的亚纯函数及其ｎ阶导数具有公共值的唯一性得到了一个一般性定理,改进并推广了许多先前已知的结果。     

On Uniqueness of Meromorphic Functions That Share Two Values

A problem of meromorphic functions that share two values is discussed, and two results recently obtained respectively by Yi H. X. and Song G. D. ＆ Li N. are improved.     

关于亚纯函数的唯一性定理

本文研究亚纯函数的唯一性问题,证明的结果与Ｈ．Ｕｅｄａ的一个工作相关。     

具有三个公共值的亚纯函数

利用权分担值的思想，对具有三个CM公共值的非常数亚纯函数的唯一性问题进行了研究，所得结果改进了Lahird的部分结论．     

共享三个值的亚纯函数的唯一性问题

This paper investigate the uniqueness problems for meromorphic functions that share three values CM and proves a uniqueness theorem on this topic which can be used to improve some previous related results.     

具有亏值的亚纯函数的唯一性

主要研究具有亏值的亚纯函数的唯一性问题,所得结果推广和改进了H.Ueda及仪洪勋等人的有关结果。     

CM分担三个公共值的亚纯函数的进一步结果

进一步研究了具有三个cM公共值的亚纯函数的唯一性，改进了H．Ueda和仪洪勋等人的有关结果．     

具有两个满亏量的亚纯函数的唯一性

本文研究了具有两个满亏量的亚纯函数的唯一性问题，推广并改进了文［１～６］的一些结果。     

导数具有公共小函数的亚纯函数

进一步讨论亚纯函数的k阶导数具有公共小函数的唯一性问题,得到两个亚纯函数唯一性问题的结果,改进了李平的有关结果.     

具有两个公共值的亚纯函数

By using the idea of weighted sharing of values, the problem of uniqueness of meromorphic functions that share two values is studied. The results in this paper improve some theorems given by M.Ozawa and Yi Hongxun et al.     

Uniqueness of Meromorphic Functions Sharing One Set

In this paper,we study uniqueness of meromorphic functions sharing one set,and obtain some results,which improve and extend the original results.     

滋长阶小于1的亚纯函数唯一性

§ 1.ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＭａｉｎＲｅｓｕｌｔｓ　ＢｙａｍｅｒｏｍｏｒｐｈｉｃｆｕｎｃｔｉｏｎｗｅａｌｗａｙｓｍｅａｎａｍｅｒｏｍｏｒｐｈｉｃｆｕｎｃｔｉｏｎｉｎｔｈｅｃｏｍｐｌｅｘｐｌａｎｅＣ .ＷｅａｓｓｕｍｅｔｈａｔｔｈｅｒｅａｄｅｒｉｓｆａｍｉｌｉａｒｗｉｔｈＮｅｖａｎｌｉｎｎａｔｈｅｏｒｙｔｈａｔｃａｎｂｅｆｏｕｎｄ ,ｆｏｒｉｎｓｔａｎｃｅ ,ｉｎ [1 ] .Ｗｅｓａｙｔｈａｔｔｗｏｍｅｒｏｍｏｒｐｈｉｃｆｕｎｃｔｉｏｎｓｆａｎｄ ｇｓｈａｒｅｔｈｅｖａｌｕｅａ∈ Ｃｐｒｏｖｉｄｅｄｔｈ…     

分担多项式的亚纯函数的进一步结果(英文)

In this paper,we use the theory of value distribution and study the uniqueness of meromorphic functions.We will prove the following result：Let f（z）and g（z）be two transcendental meromorphic functions,p（z）a polynomial of degree k,n≥max{11,k＋1}a positive integer.If fn（z）f（z）and gn（z）g（z）share p（z）CM,then either f（z）=c1ec p（z）dz, g（z）=c2e ？c p（z）dz ,where c1,c2 and c are three constants satisfying（c1c2） n＋1 c2=-1 or f（z）≡tg（z）for a constant t such that tn＋1=1.     

涉及微分多项式的亚纯函数唯一性

本文研究了[fn(f-1)m](k)和[gn(g-1)m](k)分担1CM的唯一性问题,其中f和g为超越亚纯函数.此外,我们的定理在一定程度上推广了张晓宇等人的结果。     

Meromorphic Functions That Share Fixed-Points

In this paper, we prove the following result: Let f(z) and g(z) be two nonconstant meromorphic(entire) functions, n ≥ 11(n ≥ 6) a positive integer. If fⁿ(z)f′(z) and gⁿ(z)g′(z) have the same fixed-points, then either f(z) = c₁e^cz2, g(z) = c₂e^− cz2, where c₁, c₂, and c are three constants satisfying 4(c₁c₂)^n + 1c² = −1, or f(z) ≡ tg(z) for a constant t such that t^n + 1 = 1.     

CM分担两个公共值集的亚纯函数唯一性

证明了存在一个具有2个元素的集合S_1和一个具有5个元素的集合S_2,使得对任何两个非常数亚纯函数f与g,只要满足E(S_j,f)=E(S_j,g)(j=1,2),就有f≡g.