分担四个或五个小函数的亚纯函数

本文证明了两个非常数亚约函数在具有五个ＩＭ分担小函数的前提下附加一定条件,则这两个函数必恒等,并研究了两个具有四个ＣＭ分担小函数的非常数亚纯函数之间的关系,推广了Ｎｅｖａｎｌｉｎｎａ四值定理．     

与其导数分担三个小函数的亚纯函数

主要得到亚纯函数与其导数分担三个小函数时的一个唯一性定理.     

正规函数与正规族

研究了正规函数与正规族之间的联系,利用分担集合的方法得到一族满足特殊性质p的正规函数,同时利用分担值的方法得到了一个较已有结论更为一般的结果。     

关于亚纯函数与其导函数分担小函数的一些结果

研究了亚纯函数与其导函数权分担一个小函数的唯一性问题,所得到的定理改进与推广了张继龙、杨连中(2007,2009),Li J D(2015)的结果,并回答了K.W.Yu(2003)提出的问题.     

导数具有k阶分担小函数的亚纯函数

主要讨论亚纯函数的导数具有某些k阶分担小函数时的唯一性问题,得到一个有趣的结果,推广了作者近期的一个结果..     

角域内亚纯函数的唯一性定理

该文研究了复平面上的亚纯函数在角域内分担两个集合的唯一性,将仪洪勋和林伟川最近得到的复平面上的亚纯函数在全平面上分担两个集合的唯一性定理中的在全平面上分担两个集合的条件改成在角域内分担两个集合,得到了几个唯一性定理.     

涉及分担函数的亚纯函数族的正规定则

本文得到一个涉及分担函数的亚纯函数族的正规定则：设F是区域D内的一族亚纯函数,k,l是正整数,ψ（z）季0为区域D内全纯函数,且其零点重数至多为l,如果对F中的任意函数,ff≠0,且f的所有极点重数都至少是l＋1,如果F中的任意函数f与g满足f^（k）与g^（k）在D内分担ψ（z）,那么F在D内正规．     

具有四个分担值的亚纯函数的唯一性

对给定的复数a,本文引入一个用来刻画两个亚纯函数的重数相同的公共a值点的比重的量τk,并把有关这一量与拟亏量或者权分担相结合的条件附加到两个具有四个分担值的亚纯函数上,得到了两个关于亚纯函数唯一性的定理.     

代数体函数与其导数的唯一性

通过研究代数体函数的分担值和分支点之间的关系,得到一个关于代数体函数与其导数具有公共值的唯一性定理,将Gundersen和Mues-Steinmetz关于亚纯函数与其导数的一个唯一性定理推广到代数体函数.     

两个相关亚纯函数族的正规定则

主要讨论涉及分担值的两个相关亚纯函数族的正规性,推广刘晓俊,李三华和庞学诚关于两族亚纯函数分担4个值的一个结果,给出了两个相关亚纯函数族分担3个值和2个值情况的正规定则.     

Meromorphic functions sharing small functions

Let f and g be meromorphic functions sharing four small functions a₁, a₂, a₃, a₄ a_1, a_2, a_3, a_4 ignoring multiplicities. If there is a small function a₅a_5 distinct from a_j, j=1, 2, 3, 4, a_j, j=1, 2, 3, 4, such that [`(N)](r,f=a<sub>5</sub>=g) 1 S(r,f) \overline {N}(r,f=a_5=g)\ne S(r,f) , then f=g f=g , where [`(N)](r,f=a₅=g) \overline{N}(r,f=a_5=g) is the counting function of those common zeros of f(z)-a₅(z) f(z)-a_5(z) and g(z)-a₅(z) g(z)-a_5(z) counted only once ignoring multiplicities.     

Convex functions and subharmonic functions

It is a classical result that a composition of a convex, increasing function and of a subharmonic function is subharmonic. We give related results for a composition of a convex function of several variables and of several subharmonic functions, thus imporving some recent results in this area.     

On functions behaving like additive functions

Let 0 < 1. In the paper we consider the following inequality: |f(x + y) – f(x) – f(y)| min{|f(x + y)|, |f(x) + f(y)|}, wheref: R R. Solutions and continuous solutions of this inequality are investigated. They have similar properties as additive functions, e.g. if the solution is bounded above (below) on a set of positive inner Lebesgue measure then it is continuous. Some sufficient condition for this inequality is also given.Dedicated to Professor Otto Haupt with best wishes on his 100th birthday     

On Chebyshev functions and Klee functions

Associated to a lower semicontinuous function, one can define its proximal mapping and farthest mapping. The function is called Chebyshev (Klee) if its proximal mapping (farthest mapping) is single-valued everywhere. We show that the function f is 1/λ-hypoconvex if its proximal mapping Pλf is single-valued. When the function f is bounded below, and Pλf is single-valued for every λ>0, the function must be convex. Similarly, we show that the function f is 1/μ-strongly convex if the farthest mapping Qμf is single-valued. When the function is the indicator function of a set, this recovers the well-known Chebyshev problem and Klee problem in Rn. We also give an example illustrating that a continuous proximal mapping (farthest mapping) needs not be locally Lipschitz, which answers one open question by Hare and Poliquin.     

Limiting functions of series of functions

A series with a given set of limit functions is constructed. A theorem proved by Besicovich concerning conditionally convergent series is strengthened.Translated from Matematicheskie Zametki, Vol. 10, No. 1, pp. 25–32, July. 1970.