单叶p-调和映射

主要目的是介绍两个p-调和映射类HS_p和HC_p及其相应的子类HS_p^0和H_p^0,同时研究这些类中映射的性质.首先,讨论了HS_p^0和HC_p^0中映射的几何性质.证明了在HS_p^0和HC_p^0中的映射下,单位圆盘的像域分别是星形的和凸的.其次,确定了HS_p^0、H_p^0、HS_p∩T_p和HC_p∩T_p的极值点,其中T_p表示具有非负系数的p-调和映射类.最后,证明了HC_p中映射邻域的存在性.

关于某类负系数的单叶函数

本文引入一个新的负系数函数族T(λ),0≤λ≤1。当λ=0时,T(λ)为T*,即T中的星形函数类;当λ=1时,T(λ)为Tc,即T中的凸函数类。文中笔者研究了T(λ)、T*及Tc的系数估计,偏差及覆盖定理,凸半径,极值点。

与2m特殊函数有关的解析函数类

S表示在单位圆U=z:z<1内解析函数f z=z+a2z2+…的全体所组成的类.本文引进并研究特殊解析函数类Vkλkαk=1,2,…,m,m∈N和Rkλβk有关的S的子类VRmλgk,hk;αk,kβ,ρ.讨论该类中函数的近于凸半径,结合算子理论导出类中函数的积分表达式,证明端点性质,由此推出偏差定理.

一类利用Catas算子定义的p叶解析函数类

根据Catas算子定义一类在单位圆盘U={z∈C:|z|<1}内的p叶解析函数类TS0(α,β,p,n),并利用不等式的技巧,研究它的系数不等式、星象半径、凸半径、极值点.

A Subclass of Harmonic Functions Associated with Wright’s Hypergeometric Functions

We introduce a new class of complex valued harmonic functions associated with Wright hypergeometric functions which are orientation preserving and univalent in the open unit disc. Further we define, Wright generalized operator on harmonic function and investigate the coefficient bounds, distortion inequalities and extreme points for this generalized class of functions.

α级凸象函数类的一个子类

本文引进并研究α级凸象函数类的一个子类K(λ,α),证明了包含关系和卷积定理;还得到了系数估计和偏差定理,极值点和支撑点。

再论有关α级预星象函数的一类解析函数

设A是在单位圆U=｛z：｜z｜＜1｝内解析且f（0）=f'（0）-1=0的函数f（z）的类．本文研究A的子类Qλ（α），f（z）Qλ（α）当且仅当满足条件其中Dλf（z）表示z／（1—z）λ＋1与f（z）的Hadamard卷积．对于λ＞0．0≤α＜1，得到Qλ（α）类的积分表达式、系数不等式和偏差定理；还确定了Qλ（α）类的闭凸包及其极值点和支撑点．

The Roper-Suffridge extension operator and classes of biholomorphic mappings Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

In this paper we give a survey about the Roper-Suffridge extension operator and the developments in the theory of univalent mappings in several variables to which it has led. We begin with the basic geometric properties (most of which now have a number of different proofs)and discuss relations with the theory of Loewner chains and generalizations and modifications of the operator, some of which are very recent.