1—集压缩映射的主零不动点

本文给出了１－集压缩映射的一些新的非零不动定理，它们推广和改进了［１，２，４，５］中的某些重要定理。     

L-smooth拓扑空间中的几类弱映射及其关系

给出L-smooth不定开映射和L-smooth不定闭映射以及L-smooth不定映射以及其他几种相关映射的概念．讨论它们之间的一些关系，证明与这些概念相等价的命题。     

一族OWA袋映射带有单位的若干充分条件

本文首先讨论了ＯＷＡ袋映射何时带有固定单位，给出了ＯＷＡ袋映射带有固定单位的充要条件，其次又给出了两类特殊的ＯＷＡ袋映射－ＯＣＷＡ袋映射和ＮＣＷＡ袋映射带有固定单位和自单位的若干充分条件。     

单叶调和映射

由于在极小曲面理论中的作用，对调和映射的研究已有较长时间。１９８４年以来，经典解析单叶映射的理论被推广至调和单叶映射，并获得许多结论。这些工作引起人们对它的浓厚兴趣。该文介绍这一课题某些重要成果的概貌，并指出一些尚未解决的问题。它共分六个部分：映射定理；单叶调和函数的数值估计；特殊映射；变分方法；境界性质和在极小曲面中的应用。     

带有单模糊映射的一般变分不等式解的存在性

众所周知，在各种变分不等式问题中，解的存在性是最基础也是最重要的问题之一．本文的目的是在Hilbert空间中研究带有单模糊映射的一般变分不等式解的存在性．此外，还讨论了几种特殊情况．     

趣说函数

函数是一种特殊的映射，当A，B是非空的数的集合时，映射f：A→B就叫做从A到B的函数，记作y=f（x），其中x∈A，y∈B．     

1序列覆盖映射的注记

本文的主要结果是构造两个例子分别说明1序列覆盖的商映射未必是弱开映射，度量空间上的序列覆盖π映射未必是1序列覆盖映射。     

一类圆周自映射的伪轨跟踪性质

本研究圈周上的连续自映射，我们得到一类非满映射具有伪轨跟踪性质的充分必要条件。     

环的自映射的最少周期点数

设Ｘ是一个紧致连通的ＡＮＲ＇ｓ，ｆ：Ｘ→Ｘ是连续映射。于是ｆ有Ｎｉｅｌｓｅｎ型数，ＮＦｎ（ｆ），它是数集｛＃Ｆｉｘ（ｇ＾ｎ）ｇ－ｆ｝的下界。本文在Ｘ是环时，给出ＮＦｎ（ｆ）是该数集的下确界，即存在连续映射ｇ＝ｆ，使得＃Ｆｉｘ（ｇ＾ｎ）＝ＮＦｎ（ｆ）的一个充分条件。     

万有Teichmuller空间中测地线的不唯一性

本文主要讨论万有Ｔｅｉｃｈｍｔｉｌｌｅｒ空间中的测地线问题，并给出了一些测地线不唯一的判断准则．特别地，证明了如下定理：设ｆ是单位圆△到自身上的极值拟共形映射，μ是它的复特征，如果存在常数ｋ．＜｜｜μ｜｜＿∞，使集合｛ｚ∈△：｜μ（Ｚ）｜≤ｋ｝有内点，则在万有Ｔｅｉｃｈｍｕｌｌｅｒ空间中，原点［０］与［μ］之间存在无穷多条测地线．     

单位圆盘到自身的调和映照的傅立叶系数估计

利用函数论的一般方法给出单位圆盘到自身的调和映照的傅立叶系数的界限,改进并推广了P.Duren和王晓英的相关结果.     

Harmonic mappings onto stars

A general version of the Radó-Kneser-Choquet theorem implies that a piecewise constant sense-preserving mapping of the unit circle onto the vertices of a convex polygon extends to a univalent harmonic mapping of the unit disk onto the polygonal domain. This paper discusses similarly generated harmonic mappings of the disk onto nonconvex polygonal regions in the shape of regular stars. Calculation of the Blaschke product dilatation allows a determination of the exact range of parameters that produce univalent mappings.     

平面上具有有界Fréchet导数的调和映照单叶半径的精确估计

给定单位圆盘D={z||z|1}上调和映照f(z)=h(z)+g(z),其中h(z)和g(z)为D上的解析函数,满足f(0)=0,λf(0)=1,ΛfΛ.通过引入复参数λ,|λ|=1,本文研究调和映照Fλ(z)=h(z)+λg(z)和解析函数Gλ(z)=h(z)+λg(z)的性质,得到Fλ(z)和Gλ(z)单叶半径的精确估计.作为应用,本文得到单位圆盘D上某些K-拟正则调和映照Bloch常数的更好估计,改进和推广由Chen等人所得的相应结果.     

The Distortion Theorems for Harmonic Mappings with Negative Coefficient Analytic Parts

Some sharp estimates for coefficients, distortion and the growth order are obtained for harmonic mappings $f ∈ TL^α_H$which are locally univalent harmonic mappings in the unit disk $\mathbb{D}:=\{z:|z| < 1\}$. Moreover, denoting the subclass $TS^α_H$ of the normalized univalent harmonic mappings, we also estimate the growth of $|f|,$ $f ∈ TS^α_H,$ and their covering theorems.     

The Distortion Theorems for Harmonic Mappings with Negative Coefficient Analytic Parts

Some sharp estimates for coefficients, distortion and the growth order are obtained for harmonic mappings $f \in TL^{\alpha}_H,$ which are locally univalent harmonic mappings in the unit disk $\mathbb{D}:=\{z:|z|<1\}.$ Moreover, denoting the subclass $TS^{\alpha}_H$ of the normalized univalent harmonic mappings, we also estimate the growth of $|f|,$ $f \in TS^α_H,$ and their covering theorems.     

Uniformly locally univalent harmonic mappings associated with the pre-Schwarzian norm

In this paper, we consider the class of uniformly locally univalent harmonic mappings in the unit disk and build a relationship between its pre-Schwarzian norm and uniformly hyperbolic radius. Also, we establish eight ways of characterizing uniformly locally univalent sense-preserving harmonic mappings. We also present some sharp distortions and growth estimates and investigate their connections with Hardy spaces. Finally, we study subordination principles of norm estimates.     

Covering and distortion theorems for planar harmonic univalent mappings

In this paper, we investigate Clunie and Sheil-Small’s covering theorems for sense-preserving planar harmonic univalent mappings defined in the unit disk. Our results significantly improve the earlier known result. Also, we obtain a distortion theorem for fully starlike harmonic mappings in the unit disk.     

A constructive method for starlike harmonic mappings

Summary The idea initiated by Opfer for constructing conformal mappings from the disk onto starlike domains is generalized for univalent harmonic mappings. This is of some interest, since such mappings are not characterized by analytic means.This work was supported in partsby a Promotion of Research Grant from the TECHNION, Haifaby an Undergraduate Student Research A ward from the NSERCby grants from the NSERC and the FCAR     

On harmonic K-quasiconformal mappings associated with asymmetric vertical strips

In this paper,we discuss the sense-preserving univalent harmonic mappings from the unit disk D onto asymmetrical vertical strips Ω_α={ω:α-π/2sinαR(ω)α/2sinα},π/2≤απSuch results as analytic representation formula,coefficient estimates,distortion theorem and area theorem are derived.     

The Coefficient Inequalities for a Class of Holomorphic Mappings in Several Complex Variable

The authors establish the coefficient inequalities for a class of holomorphic mappings on the unit ball in a complex Banach space or on the unit polydisk in $\mathbb{C}^n$, which are natural extensions to higher dimensions of some Fekete and Szeg\"o inequalities for subclasses of the normalized univalent functions in the unit disk.