A RANDOM FIXED POINT ITERATION FOR THREE RANDOM OPERATORS ON UNIFORMLY CONVEX BANACH SPACES

In the present paper we introduce a random iteration scheme for three random operators defined on a closed and convex subset of a uniformly convex Banach space and prove its convergence to a common fixed point of three random operators. The result is also an extension of a known theorem in the corresponding non-random case.

各向异性Banach空间值Musielak-Orlicz空间的嵌入性、紧性和一致凸性

本文给出一个各向异性的Banach空间值Musielak-Orlicz空间嵌入到另一个各向异性的Banach空间值Musielak-Orlicz空间的充分必要条件,各向异性的Banach空间值Musielak-Orlicz空间的子集为相对紧的充分必要条件以及各向异性的Banach空间值Musielak-Orlicz空间为一致凸的刻画.

STRONG CONVERGENCE OF APPROXIMATED SEQUENCES FOR NONEXPANSIVE MAPPINGS IN BANACH SPACES

This paper studies the convergence of the sequence defined by x0 ∈ C, xn＋l =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 THE EXISTENCE OF COMMON FIXED POINTS FOR A PAIR OF LIPSCHITZIAN MAPPINGS IN BANACH SPACES

The existence of common fixed points for a pair of Lipschitzian mappings in Banach spaces is proved. By using this result, some common fixed point theorems are also established for these mappings in Hilbert spaces, in L p spaces, in Hardy spaces H p, and in Sobolev spaces H r,p , for 1<p<+∞ and r≥0.

A one-step implicit iterative method for two finite families of asymptotically nonexpansive mappings in a hyperbolic space

We introduce a one-step implicit iterative method for two finite families of asymptotically nonexpansive mappings in a hyperbolic space and use it to approximate common fixed points of these families. The results presented in this paper are new in the setting of hyperbolic spaces. On top, these are generalizations of several results in literature from Banach spaces to hyperbolic spaces. At the end of the paper, we give an example to validate our results.

Property A_(UB) of Metric Spaces under Decompositions of Finite Depth

Property AUB is the notion in metric geometry which has applications in higher index problems.In this paper,the permanence property of property AUB of metric spaces under large scale decompositions of finite depth is proved.

COVERING PROPERTIES ON H-SPACES AND APPLICATIONS

Several theorems on closed (resp. open) covering properties of H-spaces are obtained which improve and generalize the corresponding results of Sperner, Klee, Alexandroff-Pasynkoff, Berge, Ghouila-Houri, Danzer-Grunbaum-Klee, Ky Fan, Shih-Tan, Horvath and Lassonde. As application an almost fixed point theorem for lower semi-continuous map in l.c.-spaces and a generalization of Tychonoffs fixed point theorem are proved in l.c.-spaces which improve those results of Ky Fan and Horvath.

相关于增长函数的非交换Orlicz空间的一致凸性

相关于增长函数的非交换Orlicz空间是拟Banach空间,研究了这类拟Banach空间的一致凸性.首先,得到了这类空间上的模和Luxemburg拟范数的控制关系.其次,给出了这类空间的一致凸性,并且估计了凸性的模.最后,给出了满足假设的具体空间的例子.

Non-expansive Mappings and Iterative Methods in Uniformly Convex Banach Spaces

In this article,we will investigate the properties of iterative sequence for non-expansive mappings and present several strong and weak convergence results of successive approximations to fixed points of non-expansive mappings in uniformly convex Banach spaces.The results presented in this article generalize and improve various ones concerned with constructive techniques for the fixed points of non-expansive mappings.

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.

Coarse Embedding into Uniformly Convex Banach Spaces

In this paper, the author studies the coarse embedding into uniformly convex Banach spaces. The author proves that the property of coarse embedding into Banach spaces can be preserved under taking the union of the metric spaces under certain condi- tions. As an application, for a group G strongly relatively hyperbolic to a subgroup H, the author proves that B（n） = {g ∈ G／ │g│suЭe≤ n} admits a coarse embedding into a uniformly convex Banach space if H does.

The Arc Distortion in QH Inner ψ-uniform （or Convex） Domains in Real Banach Spaces

Let D and D＇ be domains in real Banach spaces of dimension at least 2. The main aim of this paper is to study certain arc distortion properties in the quasihyperbolic metric defined in real Banach spaces. In particular, when D＇ is a QH inner C-uniform domain with C being a slow （or a convex domain）, we investigate the following： For positive constants c, h, C, M, suppose a homeomorphism f ： D → D＇ takes each of the 10-neargeodesics in D to （c, h）-solid in D＇. Then f is C-coarsely M- Lipschitz in the quasihyperbolic metric. These are generalizations of the corresponding result obtained recently by Viiisiilg.

线性距离空间的一致凸性与自反性

本文研究了线性距离空间的一致凸性与自反性,同时对吴从炘等提出的严格缩条件能否去掉的问题给出了肯定的答案。

局部凸空间的一致光滑性

给出局部凸空间一致光滑的一个充分条件

局部凸空间的平均局部一致凸性和一致光滑性

引进局部凸空间平均局部一致凸性的概念,给出其对偶的定义,即局部凸空间平均局部一致光滑性,并在P-自反的条件下得到它们之间的对偶定理,即(X,P)是平均局部一致凸(平均局部一致光滑)的当且仅当(X′,P′)是平均局部一致光滑(平均局部一致凸)的.

关于平均一致凸Banach空间

给出平均一致凸Ｂａｎａｃｈ空间的定义，证明了一致凸Ｂａｎａｃｈ空间是平均一致凸Ｂａｎａｃｈ空间，平均一致凸Ｂａｎａｃｈ空间是自反和弱局部一致凸Ｂａｎａｃｈ空间，并且平均一致凸Ｂａｎａｃｈ空间Ｘ中任意元在Ｘ的闭凸子集中存在唯一的最佳逼近元．

乘积G-凸空间上两个集值映象簇的重合定理(英文)

利用连续选择定理和乘积局部G 凸一致空间上的聚合不动点定理,对定义在乘积G 凸空间上的两个集值映象簇证明某些新的重合点定理.这些定理改进,统一和推广了最近文献中的很多重合点定理.

矢值序列空间ss(E_k)的正规结构和中点局部一致凸

矢值序列空间ss(Ek)是Banach序列空间lp(Ek)的重要推广 .本文讨论了ss(Ek)的正规结构和中点局部一致凸 .

Banach空间值鞅变换的有界性及其应用

本文给出关于Banach空间值鞅变换算子有界性的一种新的处理方法,得到一系列带有广泛性的结果,并应用鞅变换算子的有界性刻画了Banach空间的一致光滑性和一致凸性,使得许多已有文献中的结论成为本文的特例.

广义和强广义一致凸Banach空间

引入了广义一致凸Banach空间和强广义一致凸Banach空间的概念,证明了一致凸Banach空间是强广义一致凸Banach空间,广义一致凸Banach空间X是弱局部一致凸和严格凸的;X中任一元在以0为顶点的闭凸锥中有惟一最佳逼近;强广义一致凸Banach空间中任一元在其闭凸子集中有惟一的最佳逼近元。