Normality of meromorphic functions with multiple zeros and shared values

In this paper, we study the normality of a family of meromorphic functions and general criteria for normality of families of meromorphic functions with multiple zeros concerning shared values are obtained.     

一类亚纯函数的正规定则

该文研究了一类亚纯函数的一般性的正规定则.其结果推广了以前与之相关的一系列结果.     

Normal Families of Meromorphic Functions

In this paper, we study the normality of a family of meromorphic functions and general criteria for normality of families of meromorphic functions. Received: January 5, 2006 This research is supported by the National Natural Science Foundation, grant 10271122.     

Normal criteria for families of meromorphic functions

By using the Nevanlinna theory, we prove some normality criteria for a family of meromorphic functions under a condition on differential polynomials generated by the members of the family.     

亚纯函数族的几个正规定则

研究了亚纯函数族的正规族问题.利用Zalcman引理的方法,获得了亚纯函数族的几个正规定则.并改进了相关文献的结论.     

Two normality criteria and the converse of the Bloch principle

We prove two normality criteria for a family of meromorphic functions satisfying a certain differential condition and provide a counterexample to the converse of the Bloch principle.     

Normality and sharing functions

In this paper, we proved some normality criteria for a family of meromorphic functions, where a holomorphic function is shared by every function from the family and a linear differential polynomial generated by the members of the family.     

关于亚纯函数的正规族

在本文研究了亚纯函数族的正规族问题,利用Zalcman引理的方法,获得了亚纯函数族的几个正规定则.并改进了顾永兴和Bergweiler的结果.     

涉及微分多项式的亚纯函数的正规族

本文通过研究亚纯函数的正规族.利用反证法,获得了一个与分担值有关的涉及微分多项式的一般性的正规定则,改进了方明亮和L.Zalcman在2002年得到的一个结果.     

On normal families of meromorphic functions

In this paper, we study the normality of a family of meromorphic functions and obtain some normality results for meromorphic functions, which improve and generalize the related results of Gu, Bergweiler and Lin.     

Normal family of quasimeromorphic mappings

The more general quasimeromorphic mappings are studied with the geometric method. The necessary and sufficient conditions for the normality of the family of quasimeromorphic mappings are discussed. We proved two inequalities on the covering surface and obtained some normal criteria on quasimeromorphic mappings with them. Obviously, these criteria hold for meromorphic functions.     

涉及零点重数的亚纯函数的值分布

本文研究涉及零点重数的亚纯函数的值分布，证明了几个一般的模分布定理及相应的亚纯函数族的正规定则．     

Picard values and normal families of meromorphic functions with multiple zeros

In this paper, general modular theorems are obtained for meromorphic functions and their derivatives. The related criteria for normality of families of meromorphic functions are proved. Research supported by the National Science Foundation of China     

Hyperbolic metric and normal family

In this paper, we study the normality of the family of meromorphic functions from the viewpoint of hyperbolic metric. Then, a new sufficient and necessary condition is obtained, which can determine a given family of meromorphic functions is normal or not.     

NORMALITY CRITERIA FOR FAMILIES OF MEROMORPHIC ALGEBROID FUNCTIONS

By using the definition of Hausdorff distance, we prove some normality criteria for families of meromorphic algebroid functions. Some examples are given to complement the theory in this article.     

Normal families and exceptional functions

In this paper, we obtain some normality criteria for families of meromorphic functions that concern the exceptional functions of derivatives.     

分担函数集的正规定则

本文将亚纯函数正规性与分担函数集相结合,探讨了亚纯函数族F正规与F中任意两个函数f与g分担函数的个数,f与其导数f'分担函数的个数及函数f的重值的个数三者之间的关系,给出了一个综合判定亚纯函数族正规的充分条件.     

Normality and Montel’s Theorem

In this article, we prove a normality criterion for a family of meromorphic functions having zeros with some multiplicity which involves sharing of a holomorphic function by the members of the family. Our result generalizes Montel’s normality test in a certain sense.     

与分担函数相关的正规定则

本文研究了与分担函数相关的亚纯函数族的正规性的问题.利用Nevanlinna理论的方法,得到了一个正规定则,推广了庞学诚和Zalcman~[3]的一个结果.     

Differential polynomials and normal families

This paper continues the researches of Yang Lo and others, and gives a further generalization of Gu's criterion for the normality of a family of meromorphic functions.