L_p中渐近半收缩映象拟Ishikawa迭代过程的收敛性

在Ｌｐ中研究渐近半收缩映象拟Ｉｓｈｉｋａｗａ迭代过程的强收敛性．     

微分包含系统中的分歧问题

本文研究了包含系统O∈F(λ,x)的解集结构,给出该系统发生分歧的充分必要条件。     

关于非零解与固有元的若干问题

本文用适当的ｆｐ－同伦方法，构造若干特定泛函，在边界条件（ＭＳ，Ａ，ａ，Ｃ ）与（ＣＳ；Ａ，ａ）等的支持下，研究一类集要值映象方程的非零解，固有元等有关问题，发展了Ｓｍａｒｔ，Ｐｏｔｔｅｒ Ｂｒｏｗｄｅｒ等及作者的某些结果。     

Banach空间中渐近非扩张映象的收敛性定理

本文在Banach空间中引入和研究渐近非扩张映象及非扩张映象的某些类型的迭代序列的收敛性,其结果改进和推广了最新的一些结果,     

渐近非扩张映象具误差的迭代序列的收敛性

在Banach空间中引入渐近非扩张映象和非扩张映象某些类型的具误差的迭代序列,并研究了这些迭代序列的收敛性问题.本文的结果改进、推广和完善了最新的一些结果.     

Φ-伪压缩型映象的具误差的Ishikawa和Mann迭代程序的收敛性问题

引入Φ＿ 伪压缩型映象的概念，并研究了此类映象的具误差的Ｉｓｈｉｋａｗａ 和Ｍａｎｎ 迭代程序的收敛性问题·　本文结果改进和发展了许多人的最新结果·     

广义概率A—proper 映象的拓扑度及其不动点定理

本文建立了M—PN 空间中广义概率A-proper 映象的拓扑度及其不动点定理。它是广义A—proper 映象及其不动点定理的推广。     

半非紧测度与集值AM映象

本文以半非紧测度为工具研究一类非线性集值映象的性质，然后把所得结果用于证明微分包含的解的存在性     

一类Krasnoselskii型不动点定理

本文给出两个新的不动点定理,其推广了著名的Krasnoselskii型的不动点定理及[6,7,9—11]中的某些近代的结果。     

Banach空间中关于Lipschitz φ-半压缩映象的带误差项的Ishikawa迭代过程

本文在任意Ｂａｎａｃｈ空间中研究了Ｌｉｐｓｃｈｉｔｚ φ－半压缩映象与φ－强拟增生映象的带误差项的Ｉｓｈｉｋａｗａ迭代过程,使用新的分析技巧建立了几个强收敛定理．     

赋范空间中渐近伪压缩映象不动点的迭代逼近

设x是赋范线性空间，D是x的非空子集．设T：D→x是一个一致L—Lipschitz的渐近伪压缩映象，F(T)表T的不动点集且F(T)非空．在迭代参数(αn)和(βn)的适当假设下，证明了修改了的具有误差项的Ishikawa和Mann迭代过程强收敛于T的不动点q．几个相关结果处理赋范空间中渐近非扩张映象不动点的迭代逼近问题．所得结果改进和推广了Chang，Park和Cho，Geobel和Kirl，Liu以及Schu等人的相关结果．     

多复变量的K-拟共形映射

本文研究Cn里的单位球B到Cn里的K-拟共形全纯映射.证明的最后结果是:若f是B到Cn里的K-拟共形全纯映射,满足det(f'(0))=1,则f(B)包含一个半径至少是(CnK)1-n∫01(1+t)N-1/(1-t)2exp{-(n+1)t/1-t}dt的单叶球,其中Cn>1是只依赖于n的常数,当n→∞时,Cn→(10)~(1/2).     

On a subclass of quasi-convex mappings

A class of biholomorphic mappings named “quasi-convex mappings of type D” is introduced in the unit ball of a complex Banach space, which is the natural generalization of the convex functions in one variable. It is proved that this class of mappings is a subset of the class of “quasi-convex mappings of type A” introduced by K.A. Roper and T.J. Suffridge.     

渐近非扩张非自映射的收敛定理(英文)

设E是实的一致凸Banach空间,K是E的一个非空闭凸集,P是E到K上的非扩张的保核收缩映射.设T1,T2,T3:K→E分别是具有数列{hn},{ln},{kn}[1,∞)的渐近非扩张非自映射,使得sum (hn-1) from n=1 to ∞<∞,sum ((ln-1)) from n=1 to ∞<∞及sum (n=1(kn-1) from n=1 to ∞<∞,且F=F(T1)∩F(T2)∩F(T3)={x∈K:T1x=T2x=T3x}≠Ф.定义迭代序列{xn}:x1∈K,xn+1=P((1-αn)xn+αnT1(PT1)n-1yn),yn=P((1-βn)xn+βnT2(PT2)n-1zn),zn=P((1-γn)xn+γnT3(PT3)n-1xn),其中{αn},{βn},{γn}[ε,1-ε],ε是大于零的实数.(i)如果T1,T2,T3中有一个是全连续的或者半紧的,则{xn}强收敛于某一点q∈F;(ii)如果E具有Frechet可微范数或者满足Opial’s条件或者E的对偶空间E~*具有Kadec-Klee性质,则{xn}弱收敛于某一点q∈F.     

Banach空间中一类混合映射不动点的Ishikawa迭代逼近问题

设E为一致光滑Banach空间,K为E的非空闭凸子集,T:K→K为Φ-强伪压缩映射.其中T=T1+T2,T1:K→K为Lipschitz映射,T2:K→K为具有有界值域映射.设{αn}n∞=0和{βn}n∞=0是[0,1]中满足一定条件的两实数列.则Ishikawa迭代序列{xn}∞n=0强收敛于T的唯一不动点.     

Existence of invariant curves with prescribed frequency for degenerate area preserving mappings

We consider small perturbations of analytic non-twist area preserving mappings, and prove the existence of invariant curves with prescribed frequency by KAM iteration. Generally speaking, the frequency of invariant curve may undergo some drift, if the twist condition is not satisfied. But in this paper, we deal with a degenerate situation where the unperturbed rotation angle function r → ω + r²ⁿ⁺¹ is odd order degenerate at r = 0, and prove the existence of invariant curve without any drift in its frequency. Furthermore, we give a more general theorem on the existence of invariant curves with prescribed frequency for non-twist area preserving mappings and discuss the case of degeneracy with various orders.     

On growth and covering theorems of quasi-convex mappings in the unit ball of a complex banach space

A class of biholomorphic mappings named “quasi-convex mapping” is introduced in the unit ball of a complex Banach space. It is proved that this class of mappings is a proper subset of the class of starlike mappings and contains the class of convex mappings properly, and it has the same growth and covering theorems as the convex mappings. Furthermore, when the Banach space is confined to ℂⁿ, the “quasi-convex mapping” is exactly the “quasi-convex mapping of type A” introduced by K. A. Roper and T. J. Suffridge.     

On Decomposition Theorem of normalized biholomorphic convex mappings in Reinhardt domains

The construction of normalized biholomorphic convex mappings in the Reinhardt domain Dp = of Cn is discussed. The authors set up a Decomposition Theorem for such mappings. As a special case, it is proved that, for each such mapping f, the first k-terms of the homogeneous expansion of its j-th component fj, j = 1, 2, ... ,n, depends only on zj, where k is the number that satisfies k 相似文献   

Complete Quasiconvex Mappings in Polydisc

In this paper, a class of biholomorphic mappings called complete quasiconvex mappings is introduced and studied in bounded convex Reinhardt domains of ℂ ⁿ . Through a detailed analysis of the analytic characterization for this class of mappings, it is shown that this class of mappings contains the convex mappings and is also a subset of the class of starlike mappings. In the special case of the polydisc, a decomposition theorem is established for the complete quasiconvex mappings, which in turn is used to derive an improved sufficient condition for the convex mappings. Translated from Chinese Annals of Mathematics (Series A)