置换空间P_XX_n的范数k-粗性

利用Banach空间理论的方法,主要研究了k-粗性和k-强粗性从Banach空间Xn到置换空间PXXn上的提升问题,证明了这两种k-粗性都可以在置换空间PXXn上得到提升.     

Musielak-Orlicz序列空间的粗性

作者给出赋Luxemburg范数Musielak-Orlicz序列空间光滑点的支撑泛函的刻画．进一步,给出赋Orliez范数和赋Luxemburg范数Musielak-Orlicz序列空间的粗性,点态粗的充分必要条件．     

度量空间的序列商,k-映象

本文给出了度量空间序列商．肛映象的-些内部刻画。证明了空间X是度量空间的序列商。肛映象当且仅当X具有紧有限k-闭cs*-覆盖列的点星sn-网，当且仅当X具有紧有限k-闭覆盖列的点星网．作为上述结果的-个推论．不仅得到了空间X是度量空间序列商，k-映象当且仅当X是度量空间的k-映象，而且还证明了空间X是度量空间当且仅当X具有局部有限(紧有限)闭(肛闭)覆盖列的点星弱邻域网．这里“闭”(“k闭”)不能省略．     

二次对偶空间的k-光滑性特性

深入研究了Banach空间X的二次对偶空间的k-光滑性,给出了Banach空间X的二次对偶空间为k-光滑的若干特征刻画.     

关于k-圆形模和k-凸性模

本文证明:(ⅰ)Banach空间X为k-一致圆当且仅当它k-一致凸;(ⅱ)一列Banach空间{X_i}_(i=1)∞的l~p-乘积空间是k一致圆当且仅当存在n_0,当n>n_0时,X_n为一致圆且具共同凸性模,当1≤n≤n_0时,X_n为k_n-一致圆,且sum from n=1 to n_0 (k_n≤k+n_0-),另外,文中还对k一致圆空间中无条件收敛级数进行了讨论。     

具有CF性质的k-半分层空间

给出了k-空间类中具有CF性质的k-半分层空间的一些刻画,证明了k-空间X是具有CF性质的k-半分层空间当且仅当X具有σ-CF闭伪基(闭k-网).作为这个结果的一个应用,本文部分正面回答了k-半分层空间的两个问题.     

关于k-消去二分图的一些结果

图 G的一个 k-正则支撑子图称为 G的 k-因子 ,若对 G的任一边 e,图 G- e总存在一个 k-因子 ,则称 G是 k-消去图 .证明了二分图 G=( X,Y) ,且 | X | =| Y|是 k-消去图的充分必要条件是 k| S|≤ r1 + 2 r2 +…+ k( rk+… + rΔ) - ε( S)对所有 S X成立 .并由此给出二分图是 k-消去图的充分度条件 .     

k-控制阵

给出k-控制阵的定义,讨论k-控制阵与k-圈控制阵的关系,指出k-控制阵的周期是k的一个因子,指数不大于(n-1)k m.     

关于拟k-连通图的一个注释

G是一个k-连通图,T是G的一个k-点割,若G-T可被划分成两个子图G1,G2,且|G1 |≥2,|G2 |≥2,则称T是G的一个非平凡点割.假定G是一个不含非平凡(k-1)点割的(k-1)-连通图,则称G是一个拟k-连通图.证明了对任意一个k≥5且t＞k/2的整数,若G是一个不含(K2+tK1)的k-连通图,且G中任...     

关于Banach空间的k-光滑性

本文研究了k-光滑的Banach空间,引入了k-G可微性的概念.得到了k-光滑的Banach空间的几个等价条件.     

APPROXIMATION OF COMMON FIXED POINT OF FAMILIES OF NONLINEAR MAPPINGS WITH APPLICATIONS

It is our purpose in this paper to show that some results obtained in uniformly convex real Banach space with uniformly G?ateaux differentiable norm are extendable to more general reflexive and strictly convex real Banach space with uniformly G?ateaux differentiable norm. Demicompactness condition imposed in such results is dispensed with. Furthermore,Applications of our theorems to approximation of common fixed point of countable infinite family of continuous pseudocontractive mappings and approximation of common solution of countable infinite family of generalized mixed equilibrium problems are also discussed. Our theorems improve, generalize, unify and extend several recently announced results.     

迭代逼近m-增生映象的零点

设E是具有一致正规结构的实Banach空间,其范数是一致Gateaux可微的.设A是m-增生映象,使得C=■是E的凸子集,数列{α_n)■[0,1],{r_n}■ (0,∞),在适当的条件下,则由(1.2)式定义的迭代序列{x_n}强收敛于A~(-1)(0)中的点.其次证明了:设E是一致凸Banach空间,其范数是Frechet可微的.设数列{α_n},{β_n)■(0,1),{r_n}■(0,∞),满足适当的条件.如果A~(-1)(0)∩B~(-1)(0)≠φ,则由(3.20)式定义的序列{x_n}弱收敛于A~(-1)(0)∩B~(-1)(0)中的点.其结果推广和改进了Kamimura,Takahashi(2000)的定理2及Xu H.K.(2006)的定理4.1,定理4.2和定理4.3:(i)Kamimura,Takahashi(2000)定理2中的假设"自反Banach空间E的每个有界闭凸子集对非扩张自映象有不动点性质"被去掉;(ii)Xu H.K.(2006)的假设"E是具有弱连续对偶映象J_φ的自反Banach空间",被本文的假设"E是具有一致正规结构且其范数是一致Gateaux可微的Banach空间"所取代.从而补充了Xu H.K.(2006)未包含的另外一些Banach空间.同时还证明了逼近两个m-增生映象的公共零点,其结果也推广和改进了Mainge的相应结果.     

Strongly extreme points in Banach spaces

In this paper some properties of a special type of boundary point of convex sets in Banach spaces are studied. Specifically, a strongly extreme point x of a convex set S is a point of S such that for each real number r>0, segments of length 2r and centered x are not uniformly closer to S than some positive number d(x,r). Results are obtained comparing the notion of strongly extreme point to other known types of special boundary points of convex sets. Using the notion of strongly extreme point, a convexity condition is defined on the norm of the space under consideration, and this convexity condition makes possible a unified treatment of some previously studied convexity conditions. In addition, a sufficient condition is given on the norm of a separable conjugate space for every extreme point of the unit ball to be strongly extreme.     

关于渐近非扩张映象的强收敛定理

在具有一致正规结构且其范数是一致Gateaux可微的实Banach空间中,为寻求渐近非扩张半群的公共不动点,引入了一种新的迭代序列.在适当的条件下,用迭代逼近算法,证明了逼近于这一公共不动点的某些强收敛定理.其结果也推广和改进了引文中相应的结果.     

凸性与度量投影的连续性

本文研究近强凸、近非常凸Banach空间中度量投影的连续性。获得如下结果：若A是近强凸（近非常凸）空间中的逼近凸集,则度量投影PA是范-范上半连续的（范-弱上半连续的）。此外,我们还利用度量投影的连续性给出Banach空间为近强凸、近非常凸的一些充分必要条件。     

The Norm of a Complex Banach Lattice

In this note we study the problem how the complexification of a real Banach space can be normed in such a way that it becomes a complex Banach space from the point of view of the theory of cross-norms on tensor products of Banach spaces. In particular we show that the norm of a complex Banach lattice can be interpretated in terms of the l-tensor product of real Banach lattices.     

Banach空间中渐近非扩张强连续半群不动点的粘性逼近

在具有一致Gateaux可微范数的Banach空间中,讨论了一个逼近渐近非扩张强连续半群不动点的两步粘性逼近方法,并在一定条件下证明了该方法所得到的迭代序列的强收敛性.     

Very smooth points of spaces of operators

In this paper we study very smooth points of Banach spaces with special emphasis on spaces of operators. We show that when the space of compact operators is anM-ideal in the space of bounded operators, a very smooth operatorT attains its norm at a unique vectorx (up to a constant multiple) andT(x) is a very smooth point of the range space. We show that if for every equivalent norm on a Banach space, the dual unit ball has a very smooth point then the space has the Radon-Nikodym property. We give an example of a smooth Banach space without any very smooth points.     

Certain Fixed Point Theorems and Application to the Fractal Space

In this paper, we present some important generalizations of the Banach contraction principle, in which the Lipschitz constant k is replaced by some real-valued control function. For the applications to...     

非扩张映射不动点的粘性逼近方法

在具有一致Gateaux可微范数的Banach空间中,建立了一个改进的非扩张映射不动点的粘性逼近方法,并在一定条件下证明了该方法所得到的迭代序列的强收性.本文所得结果扩展并统一了部分文献的结果.