Zeros and fixed points of difference operators of meromorphic functions

Let f be a transcendental meromorphic function and Δf(z) = f(z + 1) − f(z). A number of results are proved concerning the existences of zeros and fixed points of Δ f(z) and Δ f(z)/f(z) when f(z) is of order σ(f)=1. Examples show that some of the results are sharp.     

On the characteristics of meromorphic functions with three weighted sharing values

In this paper, we deal with the relation between the characteristic function of two nonconstant meromorphic functions with three weighted sharing values, which improves a result given by H.X. Yi and Y.H. Li. From this we establish a theorem which improves a result given by P. Li and C.C. Yang.     

On transcendental meromorphic functions with radially distributed values

The growth of transcendental meromorphic functions in terms of their ordersis investigated in this paper when they and their derivatives have radially distributed valuesfollowing the discussion of the author. A simple and elementary way to study such subjectsis exhibited in this paper; that is, once an estimation of B(r, *) in terms of a few c(r, **) inthe Nevanlinna theory on angular domains is established, we can produce one result thatthe order of a mermorphic function with radially distributed values related to C(r, **) canbe estimated under the assumption of existence of suitable deficient value. The results ob-tained in this paper lead us to a new singular direction in terms of Nevanlinna charactersticinstead of the order of meromorphic functions.     

Some remarks on the genericity of unique range sets for meromorphic functions

In this paper we relate the study of unique range sets for meromorphic functions (URSM) with the hyperbolic hypersurfaces and give some remarks on the genericity of unique range sets for meromorphic functions.     

亚纯函数的唯一性定理

应用奈望里纳理论研究亚纯函数的唯一性问题,得到若干结果,推广了某些已知定理．     

A normal criterion about two families of meromorphic functions concerning shared values

In this paper, we mainly discuss the normality of two families of functions concerning shared values and proved: Let F and G be two families of functions meromorphic on a domain D■C,a1, a2, a3, a4 be four distinct finite complex numbers. If G is normal, and for every f ∈ F , there exists g ∈ G such that f(z) and g(z) share the values a1, a2, a3, a4, then F is normal on D.     

Completely irreducible sequences of meromorphic functions

Given a sequence {fn } of meromorphic functions on a plane domain D, there exists a (possibly empty) open set U■D and a subsequence {f n k } which converges uniformly (with respect to the spherical metric on ) on compact subsets of U, while no subsequence of {f n k } converges uniformly on compact subsets of any larger open subset of D.     

Normality and fixed-points of meromorphic functions

LetF be families of meromorphic functions in a domainD, and letR be a rational function whose degree is at least 3. If, for anyf∈ F, the composite functionR(f) has no fixed-point inD, thenF is normal inD. The number 3 is best possible. A new and much simplified proof of a result of Pang and Zalcman concerning normality and, shared values is also given.     

On multiply-connected Fatou components in iteration of meromorphic functions

Let be a transcendental meromorphic function with at most finitely many poles. We mainly investigated the existence of the Baker wandering domains of f(z) and proved, among others, that if f(z) has a Baker wandering domain U, then for all sufficiently large n, fn(U) contains a round annulus whose module tends to infinity as n→∞ and so for some 0<d<1,

     

具有两个权分担的公共值集的亚纯函数

讨论了亚纯函数分担两个集合的唯一性问题,证明了一个定理.所得结果改进了先前的一些定理,例子表明结果是精确的.     

On the family of meromorphic functions whose derivatives omit a holomorphic function

In this paper,we continue to study the normality of a family of meromorphic functions without simple zeros and simple poles such that their derivatives omit a given holomorphic function.Such a family in general is not normal at the zeros of the omitted function.Our main result is the characterization of the non-normal sequences,and hence some known results are its corollaries.     

具三个公共值的亚纯函数的唯一性

主要讨论具有三个公共值的两个亚纯函数的唯一性问题,推广并改进了H,Ueda与Brosch等人的有关结果。     

Sufficient condition for functions to be in a class of meromorphic multivalent Sakaguchi type spiral-like functions

In this article, we define a subclass of meromorphic multivalent Sakaguchi type functions and obtain certain sufficient conditions for functions to be in this class. The main result presented here includes a number of consequences as its special cases.     

CM分担三个公共小函数对的亚纯函数的惟一性

研究了具有三个CM公共小函数对，一个IM公共小函数对的亚纯函数的惟一性，改进了李平与杨重骏，Brosch等人的有关结果，用例子说明本文的结果是最佳的.     

The size of the Julia set of meromorphic functions

We give a lower bound of the hyperbolic and the Hausdorff dimension of the Julia set of meromorphic functions of finite order under very general conditions (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On normal families of meromorphic functions

T. Qian In this paper, we prove two theorems on normal families of meromorphic functions, which improve a few of results from several authors. Copyright © 2015 John Wiley & Sons, Ltd.