二阶有理迭代数列

对一类二阶有理迭代数列,通过将其化为一阶有理迭代数列并利用一阶倒数迭代数列的结论,给出了其通项公式与收敛性.     

一种生成迭代数列的新方法

围绕两个典型迭代数列的构造问题,以问题为驱动,提出一种生成迭代数列的新方法,并通过数值实验或理论证明验证迭代数列的收敛性.     

数列收敛的一个定理及其应用

数列的收敛性是数学分析的一个重要内容,对后续课程实变函数、泛函分析、实分析等的学习有很大帮助.因此,进一步深入研究数列的收敛性是有必要的.本文给出了数列收敛的一个定理及其应用.     

基于(A,η)-极大单调算子的强收敛定理

采用三步迭代算法研究(A,η)-极大单调算子的不动点问题及用预解算子研究包含问题的解.同时给出了在相关条件下,由三步迭代算法迭代产生出的数列的强收敛性.文中的算法是在Noor,Huang[1]的两步算法产生的弱收敛定理及Ram U Verma[2]的关于解决包含问题解的方法的启发下得到.     

数列极限迫敛性定理的推广(英文)

极限论是微积分中基础和重要的概念.数列极限的迫敛性定理既能判断数列的收敛性,也给出其极限值。通过对数列极限迫敛性定理的条件加以改进,得到了它的推论,并用一个例子说明了该推论的应用。     

显式迭代数列的收敛性及其推广

本文研究分别由x_(n+1)=f(x_n),x_(n+1)=f(x_n,x_(n-1)),及g(x_(n+1))=f(x_n)产生的迭代数列收敛性问题,并运用构造迭代数列的方法解决一些实际问题.     

SAOR方法的收敛性

1.引言 迭代求解线性方程组Ax=b的AOR方法已是众所周知.由AOR迭代很自然联想到构造对称AOR(SAOR)迭代,但目前讨论SAOR迭代的文章还不多见.中对系数矩阵为H阵的SAOR迭代,[6]中对系数矩阵为对称正定阵的SAOR迭代,均给出了收敛性定理.本文讨论系数矩阵为对角元素非零的相容次序阵时SAOR迭代的收敛性,得到了相应的收敛性定理,并给出了SAOR迭代矩阵谱半径表达式以及谱半径的一个上下界.     

递推数列x_(n+1)=f(x_n)的单调性与收敛性讨论

利用函数单调递增对递推数列xn+1=f(xn)单调性进行讨论,在对递推数列收敛性作分析的基础上,得到使得递推数列收敛的初始迭代值的区域,讨论的方法可以用于类似问题的研究.     

一类数列收敛性的证明

讨论由递推公式给出的一类收敛数列收敛性的证明,尤其是单调有界定理在此类问题上的应用。     

递推数列xn＋1=f（xn）的单调性与收敛性讨论

利用函数单调递增对递推数列xn＋1=f（xn）单调性进行讨论,在对递推数列收敛性作分析的基础上,得到使得递推数列收敛的初始迭代值的区域,讨论的方法可以用于类似问题的研究．     

A newer class of numerical sequences and its applications to sine and cosine series

We prove three theorems for sequences of γ group bounded variation, which are analogues of the theorems proved earlier for monotone, or quasi-monotone sequences, or sequences of rest bounded variation.     

B值随机变量序列的一类局部收敛定理

研究取值于Banach空间随机变量序列的一类局部收敛定理．作为推论,得到了一类B值鞅差序列的极限定理和经典的独立随机变量序列的极限定理,     

Almost sure central limit theorems on the Wiener space

In this paper, we study almost sure central limit theorems for sequences of functionals of general Gaussian fields. We apply our result to non-linear functions of stationary Gaussian sequences. We obtain almost sure central limit theorems for these non-linear functions when they converge in law to a normal distribution.     

On the Recurrence Set of Planar Markov Random Walks

In this paper, we investigate properties of recurrent planar Markov random walks. More precisely, we study the set of recurrence points with the use of local limit theorems. The Nagaev–Guivarc’h spectral method provides several examples for which these local limit theorems are satisfied as soon as some (standard or non-standard) central limit theorem and some non-sublattice assumption hold.     

Ratio Tauberian Theorems for Positive Functions and Sequences in Banach Lattices

We prove two ratio Tauberian theorems and deduce two generalized Tauberian theorems for functions and sequences with values in positive cones of Banach lattices. Two counter-examples are given to show that the hypotheses in the ratio Tauberian theorems are essential.     

负相关随机变量序列的对数律

在本文中,首先我们得到了负相关(ND)随机变量序列的指数不等式和矩不等式,然后运用这些不等式讨论了ND序列的对数律.结果,我们将独立情形下的对数律推广到ND序列情形下依然成立.     

B值随机变量序列的局部收敛定理

本文的目的是研究B值随机变量序列的局部收敛定理。作为推论，得到了一类B值鞅差序列的极限定理和若干经典的独立随机变量序列的极限定理。     

One-sided theorems on the law of the iterated logarithm without the independence assumption

One proves two theorems on the law of the iterated logarithm for sequences of random variables that are not necessarily independent. These theorems are the one-sided analogues of certain results of Lai and Stout.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Institua im. V. A. Steklova AN SSSR, Vol. 130, pp. 150–156, 1983.     

Convergence theorems and Tauberian theorems for functions and sequences in Banach spaces and Banach lattices

We prove generalized convergence theorems and Tauberian theorems for vector-valued functions and sequences of growth order γ − 1 with γ > 0 and for positive functions and sequences in Banach lattices. Then the general results are applied to obtain some interesting particular Tauberian results for various examples of operator semigroups. Among them are mean ergodic theorems for Cesàro-mean-bounded semigroups (discrete and continuous) of operators and for semigroups of positive operators. Research supported in part by the National Science Council of Taiwan. Current address: 19-18, Higashi-hongo 2-chome, Midori-ku, 226-0002 Japan.     

A note on the uniform convergence and boundedness of a new class of sine series

Summary A new class of sequences, broader than the class of sequences of rest bounded variation, is redefined, and the sufficient parts of three theorems pertaining to the uniform convergence or boundedness of sine series are extended to the case when the coefficients of the sine series belong to this new class.