Banach空间中全纯映射的若干性质

本文将全纯映射的若干性质推广到Ｂａｎａｃｈ空间,并应用这些性质研究有界域中的凸映射与星形映射．     

复Banach空间与平衡域上的双全纯凸映射的增长性定理

本文将利用从属原理给出双全纯凸映射的精确增长性定理．     

复Banach空间与平衡域上的双全纯凸映射的增长性定理

本文将利用从属原理给出双全纯凸映射的精确增长性定理.     

复Banach空间中单位球上双全纯凸映射的偏差定理

本文讨论一般复Banach空间上单位球B的Caratheodory度量和Kobayashi 度量的性质,并据此将Cn(n≥1)中单位球Bn上双全纯凸映射的矩阵形式偏差定理 推广到一般复Banach空间的单位球B上.     

复Banach空间单位球上准凸映射的增长定理与掩盖定理

在一般复Banach空间中的单位球上讨论了一类严格介于凸映射类与星形映射类的\"准凸映射类”, 证明了准凸映射具有与凸映射类完全相同的增长定理与掩盖定理. 同时证明了它与K. A. Roper和T. J. Suffridge在 中单位球上所定义的\"A型准凸映射类\"完全一致.     

本质上是Banach空间闭凸子集的凸度量空间

利用凸度量空间中凸结构的性质,在保持凸组合关系与等距嵌入意义下,获得了一个凸度量空间本质上是某个Banach空间中闭凸子集的充分必要条件,并举例说明了其应用.     

拟凸Hartogs域到复空间形式的全纯等距嵌入映射的存在性

在Cn中的有界拟凸Hartogs域Ω上,存在一个自然的K?hler度量gΩ．该文将研究有界拟凸Hartogs域(Ω,hgΩ)到复空间形式的全纯等距嵌入映射的存在性问题.     

关于Banach空间的强凸性

本文讨论强凸性、Ｌ－ｋＲ，ＬωＲ和（Ｇ）性质之间的关系，指出强凸性介于ＬωＲ和（Ｇ）性质之间，证明光滑的有（Ｇ）性质的Ｂａｎａｃｈ空间是强凸的，此外指出存在一个Ｂａｎａｃｈ空间Ｘ，它是ＬωＲ但对任意自然数ｋ，Ｘ不是Ｌ－ｋＲ．     

Bansch空间中全纯映射的若干性质

本文将全纯映射的若干性质推广到Ｂａｎａｃｈ空间，并应用这些性质研究有界域中的凸映射与星形映射。     

有界平衡拟凸域上星形映射的一个新特征

假定Ω是Cn中具有C2定义函数的有界平衡拟凸域本文证明Ω上的每一星形映射f能表示成schwarz映射的极限形式.作为应用,得到有界平衡拟凸域上星形映射的增长定理.最后给出星形映射的一个的等价刻画.     

m-增生算子零点的广义最速下降逼近

使用新的分析技巧研究了对于广义最速下降逼近法收敛到m-增生算子零点的充要条件,所得结果推广了几位作者早期与最近的相应结果．     

Properties for a Class of Holomorphic Mapson Hilbert Space

Itiswell-knownthattheanalyticfunctionwithpositiverealpartintheunitdiscofthecomplexplaneplaysaveryimportantroleinthegeometrictheoryofcomplexvariablefunc-tions.Ithasbeenremarkablehowtoextendtheclassicalresultofthetheoryoffunctionstoabstractspacesinrecentyears[2].Inthisnotewedefineageneralizedhalf-planeinHilbertspaceandfindthebiholomorphicmapoftheunitballonHilbertspaceontothishalf-plane.Asacorollary,wegiveashortproofofaresultin[5].UsingtheaboveholomooorphicmapweobtainthedistortiontheoremandPick…     

Normal families of holomorphic functions and mappings on a Banach space

The authors lay the foundations for the study of normal families of holomorphic functions and mappings on an infinite-dimensional normed linear space. Characterizations of normal families, in terms of value distribution, spherical derivatives, and other geometric properties are derived. Montel-type theorems are established. A number of different topologies on spaces of holomorphic mappings are considered. Theorems about normal families are formulated and proved in the language of these various topologies. Normal functions are also introduced. Characterizations in terms of automorphisms and also in terms of invariant derivatives are presented.     

k-super-strongly convex and k-super-strongly smooth Banach spaces

In this paper, we introduce two types of new Banach spaces: k-super-strongly convex spaces and k-super-strongly smooth spaces. It is proved that these two notions are dual. We also prove that the class of k-super-strongly convexifiable spaces is strictly between locally k-uniformly rotund spaces and k-strongly convex spaces, and obtain some necessary and sufficient conditions of k-super-strongly convex space (respectively k-super-strongly smooth space). Also, for each k?2, it is shown that there exists a k-super-strongly convex (respectively k-super-strongly smooth) space which is not (k−1)-super-strongly convex (respectively (k−1)-super-strongly smooth) space.     

Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces

This paper studies the convergence of the sequence defined by x0∈C,xn 1=αnu (1-αn)Txn,n=0,1,2,…, where 0 ≤αn ≤ 1, limn→∞αn = 0, ∑∞n=0 αn = ∞, and T is a nonexpansive mapping from a nonempty closed convex subset C of a Banach space X into itself. The iterative sequence {xn} converges strongly to a fixed point of T in the case when X is a uniformly convex Banach space with a uniformly Gateaux differentiable norm or a uniformly smooth Banach space only. The results presented in this paper extend and improve some recent results.     

On uniform convexity of Banach spaces

This paper gives some relations and properties of several kinds of generalized convexity in Banach spaces. As a result, it proves that every kind of uniform convexity implies the Banach-Sakes property, and several notions of uniform convexity in literature are actually equivalent.