σ,双A,Aσ-统计收敛的表示定理

证明了Banach空间X中序列{x_k},σ-统计收敛以及双序列{x_（kl）},双A和A_σ统计收敛的表示定理.     

TVS-锥度量空间中的统计收敛

本文研究TVS-锥度量空间中的统计收敛以及TVS-锥度量空间的统计完备性.令(X,E,P,d)表示一个TVS-锥度量空间.利用定义在有序Hausdorff拓扑向量空间E上的Minkowski函数ρ,证明了在X上存在一个通常意义下的度量d_ρ,使得X中的序列(x_n)在锥度量d意义下统计收敛到x∈X,当且仅当(x_n)在度量d_ρ意义下统计收敛到x.基于此,我们证明了任意一个TVS-锥统计Cauchy序列是几乎处处TVS-锥Cauchy序列,还证明了任意一个TVS-锥统计收敛的序列是几乎处处TVS-锥收敛的.从而,TVS-锥度量空间(X,d)是d-完备的,当且仅当它是d-统计完备的.基于以上结论,通常度量空间中统计收敛的许多性质都可以平行地推广到锥度量空间中统计收敛的情形.     

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(ω)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(ω)性质，那么lp(X)(1≤p＜ ∞)与c0(X)也有(ω)性质。     

关于GB型空间的若干结果

本文对GB型空间进行了若干讨论,得到了一些结果。 设X为Banach空间,X为X的共轭空间,B(X,X)为X到X的所有有界线性算子组成的空间。如果X中的弱收敛序列为弱收敛序列,则称X为GB型空间。Grothendieck.A于1953年证明了l~∞是GB型空间。显然自反空间是GB型空间。     

理想收敛与几乎处处收敛（英文）

本文试图利用统计测度理论刻画Banach空间X中的序列为理想L-几乎处处收敛的特征.设L2~N为任意一个统计型的理想,令X_L=span{χA:A∈L}e_∞,p_L为商空间e_∞/X_L的商范数,p_L(e)表示半范数p_L在e≡χN点的次微分映射.本文证明了x~*∈p_L(e)为一个端点当且仅当x~*是保正交不变的.证明了序列(x_n)→X L-几乎处处收敛于x∈X当且仅当存在(x_n)的一个子列(x_(n_k))使得x_(n_k)→x(k→∞)且对任意x~*∈extp_L(e),x~*为{e_(n_k)}的w~*-聚点,其中extp_L(e)表示集合p_L(e)的所有端点构成的集合.     

TVS-锥度量空间中的统计收敛

本文研究TVS-锥度量空间中的统计收敛以及TVS-锥度量空间的统计完备性.令（X，E，P，d）表示一个TVS-锥度量空间.利用定义在有序Hausdorff拓扑向量空间E上的Minkowski函数ρ，证明了在X上存在一个通常意义下的度量d_ρ，使得X中的序列（x_n）在锥度量d意义下统计收敛到x ∈ X，当且仅当（x_n）在度量d_ρ意义下统计收敛到x.基于此，我们证明了任意一个TVS-锥统计Cauchy序列是几乎处处TVS-锥Cauchy序列，还证明了任意一个TVS-锥统计收敛的序列是几乎处处TVS-锥收敛的.从而，TVS-锥度量空间（X，d）是d-完备的，当且仅当它是d-统计完备的.基于以上结论，通常度量空间中统计收敛的许多性质都可以平行地推广到锥度量空间中统计收敛的情形.     

Banach空间中弱收敛序列系数的估计

利用.Jordan—von Neumann型常数C_t~′(X),C_(-∞)(X)和弱正交系数μ(X)对Banach空间中的弱收敛序列系数WCS(X)进行了估计,从而得到空间具有正规结构的充分条件,这些结论推广了最近一些文献中的结果.同时,还计算了Bynum空间l_(2.∞)。中上述常数的取值,来说明我们给定的条件是一个严格的推广.     

理想收敛的若干研究及推广

在Banach空间X中利用序列的I-收敛与I*-收敛给出理想I具可加性质(AP)的等价刻画,并进一步研究弱I-收敛、弱I*-收敛、一致弱I*-收敛之间,以及弱I-收敛与收敛之间的关系,最后基于I-λ-统计收敛给出其推广:I-A-统计收敛,并以次微分映射为工具定义一族有限可加测度,用于等价刻画I-A-统计收敛,这亦是有限可加测度的一个应用体现.     

Banach空间中的kUKK性质

给出Banach空间X的一个新的几何性质—kUKK,证明了具有该性质的Banach空间X具有弱Banach-Saks性质;Banach空间X是kNUC的充分必要条件是自反且具有kUKK性质;鉴于几何常数在Banach空间几何性质中扮演的重要角色,由kUKK的定义给出了新常数R_2(X)的定义,并证明了当R_2(X)k时,Banach空间X具有弱不动点性质;最后计算R_2(X)在Cesaro序列空间中的具体值.     

广义的约当-冯诺依曼型常数和正规结构

本文引入了一个广义的约当-冯诺依曼型常数,并研究了它的相关性质,同时还利用广义的约当-冯诺依曼型常数,弱正交系数μ(X)和Domínguez-Benavides系数R(1,X),对Banach空间中的弱收敛序列系数WCS(X)进行了估计,从而得到了空间具有正规结构的一些充分条件.这些结论严格推广了最近一些文献中的结果.     

Tauberian conditions for w-almost convergent double sequences

In this paper, we introduce the concept of w-almost convergent sequences. Such a definition is a weak form of almost convergent sequences given by G. G. Lorentz in [Acta Math. 80(1948),167-190]. We give a detailed study on w-almost convergent double sequences and prove that w-almost convergence and almost convergence are equivalent under the boundedness of the given sequence. The Tauberian results for w-almost convergence are established. Our Tauberian results generalize a result of Lorentz and Tauber’s second theorem. Moreover, we prove that w-almost convergence and norm convergence are equivalent for the sequence of the rectangular partial sums of the Fourier series of f ∈ L^p(T²), where 1 < p < ∞.      

Statistical convergence of double sequences in intuitionistic fuzzy normed spaces

Recently, the concept of intuitionistic fuzzy normed spaces was introduced by Saadati and Park [Saadati R, Park JH. Chaos, Solitons & Fractals 2006;27:331–44]. Karakus et al. [Karakus S, Demirci K, Duman O. Chaos, Solitons & Fractals 2008;35:763–69] have quite recently studied the notion of statistical convergence for single sequences in intuitionistic fuzzy normed spaces. In this paper, we study the concept of statistically convergent and statistically Cauchy double sequences in intuitionistic fuzzy normed spaces. Furthermore, we construct an example of a double sequence to show that in IFNS statistical convergence does not imply convergence and our method of convergence even for double sequences is stronger than the usual convergence in intuitionistic fuzzy normed space.     

Statistically convergent difference double sequence spaces

In this article we define the notion of statistically convergent difference double sequence spaces. We examine the spaces 2l∞（△, q）, 2c（△, q）, 2cB（△, q）, 2cR（△, q）, 2cBR（△,q） etc. being symmetric, solid, monotone, etc. We prove some inclusion results too.     

L 1-convergence of double cosine- and Walsh-Fourier series

We prove the convergence inL ¹([−gp, π)²)-norm of the double Fourier series of an integrable functionf(x, y) which is periodic and even with respect tox andy, with coefficientsa _jk satisfying certain conditions of Hardy-Karamata kind, and such thata _jk logj logk→0 asj, k→∞. These sufficient conditions become quite natural in particular cases. Then we extend these results to the convergence of double Walsh-Fourier series inL ¹ (0, 1)²)- norm. As a by-product, we obtain Tauberian conditions ensuring the convergence of a double numerical series provided it is Cesàro summable. This research was partially supported by the Hungarian National Foundation for Scientific Research under Grant # 234.     

Analysis of a new class of forward semi-Lagrangian schemes for the 1D Vlasov Poisson equations

The Vlasov equation is a kinetic model describing the evolution of a plasma which is a globally neutral gas of charged particles. It is self-consistently coupled with Poisson’s equation, which rules the evolution of the electric field. In this paper, we introduce a new class of forward semi-Lagrangian schemes for the Vlasov–Poisson system based on a Cauchy Kovalevsky (CK) procedure for the numerical solution of the characteristic curves. Exact conservation properties of the first moments of the distribution function for the schemes are derived and a convergence study is performed that applies as well for the CK scheme as for a more classical Verlet scheme. A L ¹ convergence of the schemes will be proved. Error estimates [in O(Dt²+h² + \frach²Dt){O\left(\Delta{t}^2+h^2 + \frac{h^2}{\Delta{t}}\right)} for Verlet] are obtained, where Δt and h = max(Δx, Δv) are the discretization parameters.     

Two valued measure and summability of double sequences

In this paper, following the methods of Connor [2], we extend the idea of statistical convergence of a double sequence (studied by Muresaleen and Edely [12]) to μ-statistical convergence and convergence in μ-density using a two valued measure μ. We also apply the same methods to extend the ideas of divergence and Cauchy criteria for double sequences. We then introduce a property of the measure μ called the (APO₂) condition, inspired by the (APO) condition of Connor [3]. We mainly investigate the interrelationships between the two types of convergence, divergence and Cauchy criteria and ultimately show that they become equivalent if and only if the measure μ has the condition (APO₂).     

Rates of Convergence for Double Sequences

In 1900 Pringsheim presented the following definition for convergence of a double sequence (i.e. ordinary infinite matrices). A double sequence [x] has limit L if the terms of the double sequence approaches L as both the column and row indices increases. Using this notion for convergence I will present definitions for asymptotically equivalent double sequences, rate preserving four dimensional matrix transformation, and these definitions shall be used to present two natural invariance theorems.AMS Subject Classification (2000): Primary 42B15, Secondary 40C05     

Modified Lagrange–Galerkin methods of first and second order in time for convection–diffusion problems

We introduce modified Lagrange–Galerkin (MLG) methods of order one and two with respect to time to integrate convection–diffusion equations. As numerical tests show, the new methods are more efficient, but maintaining the same order of convergence, than the conventional Lagrange–Galerkin (LG) methods when they are used with either P ₁ or P ₂ finite elements. The error analysis reveals that: (1) when the problem is diffusion dominated the convergence of the modified LG methods is of the form O(h ^m+1 + h ² + Δt ^q ), q = 1 or 2 and m being the degree of the polynomials of the finite elements; (2) when the problem is convection dominated and the time step Δt is large enough the convergence is of the form O(\frach^m+1Dt+h²+Dt^q){O(\frac{h^{m+1}}{\Delta t}+h^{2}+\Delta t^{q})} ; (3) as in case (2) but with Δt small, then the order of convergence is now O(h ^m  + h ² + Δt ^q ); (4) when the problem is convection dominated the convergence is uniform with respect to the diffusion parameter ν (x, t), so that when ν → 0 and the forcing term is also equal to zero the error tends to that of the pure convection problem. Our error analysis shows that the conventional LG methods exhibit the same error behavior as the MLG methods but without the term h ². Numerical experiments support these theoretical results.     

On a generalization of a theorem of B. tyler

LetB be an arbitrary normal matrix, satisfying some conditions. AbsoluteB-summability factors in a sequence for Cesàro methodC ^α if α≧1 or α=0 and absolute convergence factors in a sequence forC ^α if 0<α<1 are obtained.     

On ideal convergence of double sequences in probabilistic normed spaces

The notion of ideal convergence is a generalization of statistical convergence which has been intensively investigated in last few years.For an admissible ideal ∮N× N,the aim of the present paper is to introduce the concepts of ∮-convergence and ∮*-convergence for double sequences on probabilistic normed spaces(PN spaces for short).We give some relations related to these notions and find condition on the ideal ∮ for which both the notions coincide.We also define ∮-Cauchy and ∮*-Cauchy double sequences on PN spaces and show that ∮-convergent double sequences are ∮-Cauchy on these spaces.We establish example which shows that our method of convergence for double sequences on PN spaces is more general.