Banach空间逼近紧性与预报算子连续性的几何条件

首先给出 Banach空间为逼近紧的几何特征 .然后用随机变量组成的 Banach空间及空间中预报集的几何性质给出预报算子连续的条件 .     

Banach空间的弱*序列紧性

本文研究了Ｂａｎａｃｈ空间的弱序列紧性．Ｂａｎａｃｈ空间Ｘ称为有（ｗ）性质，如果Ｘ（Ｘ的共轭空间）的每个有界序列有弱收敛子列．我们证明了，如果Ｂａｎａｃｈ空间Ｘ有（ｗ）性质，那么ｌｐ（Ｘ）（１≤ｐ＜＋∞）与ｃ０（Ｘ）也有（ｗ）性质．     

Countable choice and compactness

We work in set-theory without choice ZF. Denoting by the countable axiom of choice, we show in that the closed unit ball of a uniformly convex Banach space is compact in the convex topology (an alternative to the weak topology in ZF). We prove that this ball is (closely) convex-compact in the convex topology. Given a set I, a real number p1 (respectively p=0), and some closed subset F of [0,1]^I which is a bounded subset of ℓ^p(I), we show that (respectively DC, the axiom of Dependent Choices) implies the compactness of F.     

Polynomials,Symmetric Multilinear Forms and Weak Compactness

In this paper we obtain some versions of weak compactness James theorem, replacing bounded linear functionals by polynomials and symmetric multilinear forms.     

Banach空间二阶非线性混合型脉冲微分-积分方程边值问题的解

在较弱的条件下,利用MSnch不动点定理,研究了Banach空间中二阶非线性混合型脉冲微分-积分方程边值问题解的存在性,推广和改进了某些已有的结果.     

Banach空间上一类由算子导出的局部凸拓扑

本文我们研究了由半范簇｛ＰＴ｜Ｔ∈ψ（Ｅ，Ｅ１）｝在Ｅ上导出的局部凸拓扑σＥ（Ｅ１），其中ＰＴ（ｘ）＝Ｔｘ的范数，ｘ∈Ｅ。首先我们给出了拓扑σＥ（Ｅ１）＝ω和σＥ（Ｅ１）＝Ｅ上的范数的等价条件，接着讨论了在σＥ（Ｅ１）下的紧性与完备性，最后利用空间稠密特征和关于无穷基数幂等的Ｈｅｓｓｅｎｂｅｒｇ定理进一步研究了σＥ（Ｅ１）与Ｅ上的范数的关系，证明了当Ｅ的稠密特征足够大时在ω和Ｅ上的范数间有无穷多个     

Banach空间二阶积分-微分方程终值问题极值解

利用新的比较定理和半序理论,研究Banach空间二阶非线性积分-微分方程终值问题最小解和最大解的存在性,获得了新的结果.     

Loeb measure,finitely additive measures,and a theorem of Banach

The Loeb measure construction from nonstandard analysis is applied to two theorems in standard measure theory. In both cases the essential simplification offered by the approach is the ability to work with a σ-additive measure space, even if the hypotheses only guarantee finite additivity. The key to this simplification is the property of -saturated nonstandard models, that any finitely additive measure on an internal algebra extends immediately to a σ-additive measure.      

Function spaces and product topologies on powers of spaces

A study is made of two classes of product topologies on powers of spaces: the general box product topologies, and the general uniform product topologies. Some examples are given and some results are shown about the properties of these general product spaces. This is applied to show that certain spaces of continuous functions with the fine topology are homeomorphic to box product spaces, and certain spaces of continuous functions with the uniform topology are homeomorphic to uniform product spaces.     

Study of the solutions to a model porous medium equation with variable exponent of nonlinearity

The authors of this paper study the Dirichlet problem of the following equation

ut−div(|u|^ν(x,t)∇u)=f−|u|^p(x,t)−1u.     

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.     

Estimation of Mean and Covariance Operator for Banach Space Valued Autoregressive Processes with Dependent Innovations

In this paper we study autoregressive processes of order 1 with values in a separable Banach space it B. Such ARB(1)-processes are defined by the recursion equation

Banach空间单位球面的球覆盖性质

证明了n维Banach空间的单位球面最少可被2n个不含原点的半径相同的球对称覆盖,并计算了空间(Rn,‖·‖2)中,单位球面可被∪in=1B(±rxi,r)(其中r∈R ,xi∈SX)覆盖时,r的最小值是2n,且球心{xi}ni=1构成了Rn的一组正交基.     

Hoeder Continuity of Weak Solutions for Parabolic Equations with Nonstandard Growth Conditions

In this paper, we investigate the interior regularity including the local boundedness and the interior HSlder continuity of weak solutions for parabolic equations of the p（x, t）-Laplacian type. We improve the Moser iteration technique and generalize the known results for the elliptic problem to the corresponding parabolic problem.