B值独立同分布随机变元序列的矩完全收敛性

完全收敛性是概率论极限理论中一个重要的概念．本文考虑了矩完全收敛性，讨论了型-p Banach空间中独立同分布随机变元列部分和矩完全收敛性成立的充要条件，显示了矩完全收敛性和矩之间的关系，其结论与完全收敛性相比，还是有自身的特点．     

ρ混合阵列的收敛性

该文引入了ρ～混合阵列的概念，讨论了ρ～混合阵列的完全收敛性与依概率收敛性. 所得结果，推广了行独立随机变量阵列相应的结果. 此外还得到了一般随机变量阵列的完全收敛性与依概率收敛性.     

强不变原理与完全收敛性的统一形式

本文建立了强不变原理与完全收效性的统一形式，得到了用强不变原理研究完全收敛性的方法，前人许多关于强不交原理和完全收敛性的结论是本文的推论．     

两两NQD列加权和的安全收敛性

本文研究两两NQD系加权和的完全收敛性，证明了一般双下标加权系数的加权部分和的完全收敛性，改进了吴群英（2002）的结果。     

Banach空间的型与B值随机元和的完全收敛性

本文讨论了Ｂ值随机元非随机足标与随机足标和的完全收敛性．当０＜ｔ＜１时，得到了任意随机元完全收敛性的一般性结论；当１≤ｔ＜ｐ≤２时，揭示了独立零均值随机元的完全收敛性与Ｂａｎａｃｈ空间ｐ型性质的关系．推广并加强了许多熟知的结果     

两两NQD阵列加权和的收敛性质

研究了不同分布行两两NQD阵列加权和的Lp收敛性和完全收敛性，改进了前人的结果．     

ρ^ ～混合序列加权和完全收敛性和强收敛性

讨论了ρ^ ～混合序列加权和完全收敛性和强收敛性，推广了Stout和Thrum定理。     

不同分布NA序列加权和的完全收敛性

本文讨论了不同分布NA随机变量序列加权和的完全收敛性，获得了较[7]中的定理1及定理A更为一般的安全收敛性，并得到了完全收敛速度与矩条件之间的等价关系。     

B值随机元阵列的完全收敛性及大数定律

该文在随机元阵列随机有界于某非负随机变量的条件下，得到了B值随机元阵列完全收敛性的一般性结论，并讨论了随机元阵列加权和的收敛性，使[5][6]中的结果得到了改进和推广．同时讨论了完全收敛性与Banach空间p型（1＜P≤2）性质的等价性，使[14]，[15]中的结果得到进一步的改进．     

NOD随机变量序列加权和的矩完全收敛性

讨论了NOD随机变量序列加权和的矩完全收敛性,获得了NOD随机变量序列加权和的矩完全收敛性的充要条件.这些结论显示了矩完全收敛性和矩条件之间的等价关系,同时推广了Wu Qunying(2011)的结果.     

Some convergence theorems of non-implicit iteration process with errors for a finite families of I-asymptotically nonexpansive mappings

The purpose of this paper is to study the weak and strong convergence of non-implicit iteration process with errors to a common fixed point for a finite family of I-asymptotically quasi-nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of several authors [1], [2], [7], [8], [9], [10], [11], [12], [13], [14], [17], [19], [22], [23], [24], [25], [26], [27], [28] and [29].     

Weak convergence conditions for Inexact Newton-type methods

We establish a new semilocal convergence results for Inexact Newton-type methods for approximating a locally unique solution of a nonlinear equation in a Banach spaces setting. We show that our sufficient convergence conditions are weaker and the estimates of error bounds are tighter in some cases than in earlier works [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30] and [31]. Special cases and numerical examples are also provided in this study.     

The matching theorems in G-convex spaces with applications

The purpose of this paper is to establish some new matching theorems in G-convex spaces and, as applications, to obtain some new fixed point theorems, section theorems and a minimax theorem in G-convex spaces. The results presented in this paper improve and generalize the corresponding results in [1], [2], [3], [4], [5], [7], [8], [9], [10], [11] and [12].     

Global exponential stability of a class of retarded impulsive differential equations with applications

This paper studies the dynamics of a class of retarded impulsive differential equations (IDE), which generalizes the delayed cellular neural networks (DCNN), delayed bidirectional associative memory (BAM) neural networks and some population growth models. Some sufficient criteria are obtained for the existence and global exponential stability of a unique equilibrium. When the impulsive jumps are absent, our results reduce to its corresponding results for the non-impulsive systems. The approaches are based on Banach’s fixed point theorem, matrix theory and its spectral theory. Due to this method, our results generalize and improve many previous known results such as [3], [5], [6], [9], [17], [18], [23], [32], [38], [43], [51], [52]. Some examples are also included to illustrate the feasibility and effectiveness of the results obtained.     

On strong convergence in real Banach spaces obtained by dropping the Lipshitz condition

We consider an implicit iterative process for two finite families of mappings in a real Banach space and prove strong convergence results without using the Lipschitz condition on mappings. Our results mainly improve and extend the recent results of Chang et al. (2001, 2009, 2007) [1], [2], [3], Cho et al. (2005) [4], Gu (2008) [14], Ofoedu (2006) [9], Schu (1991) [13], Zeng (2003, 2005) [20], [21], and Qin et al. (2008) [11], [12].     

Convergence Theory for AOR Method

In this paper we give some sufficient conditions for the convergence of the AOR method, introduced by Hadjidimos [5], which include the ones from [1], [2], [5], [6], [7], [9], [10], [11], [12] and which show that the necessary condition given in [8] for the convergence of the AOR method is not valid. We give general conditions for the class of H-matrices, but they are not always easy to check in practice. Consequently, we give some more practical conditions concerning some subclasses of H-matrices.     

A class of norms of iterative methods for solving systems of linear equations

A new class of norms which generalize norms previously investigated by Young [9, 14], Sheldon [4, 5], Golub [1], Golub and Varga [2], Varga [6], Wachspress [7], Young and Kincaid [12], Young [14], and Kincaid [3] is introduced. Expressions for these norms applied to the matrices associated with various iterative methods are developed.Work on this paper was sponsored by NSF Grant GP-8442 and Army Grant DA-ARO(D)-31-124-G1050 at The University of Texas at Austin.     

Graphs with two isomorphism classes of spanning unicyclic subgraphs

The graphs whose spanning unicyclic subgraphs partition into exactly two isomorphism classes are characterized.This work is a continuation of [6] where graphs with one isomorphism class of spanning unicyclic graphs are characterized. The analogous question for spanning trees was posed in [10] and graphs with one isomorphism class of spanning trees were characterized in [2], [3], [4], [7], [11] while graphs with two isomorphism classes of spanning trees were characterized in [4], [5]. Related topics are treated in [1], [8], [9].     

A method for finding sharp error bounds for Newton's method under the Kantorovich assumptions

Summary This paper gives a method for finding sharpa posteriori error bounds for Newton's method under the assumptions of Kantorovich's theorem. On the basis of this method, new error bounds are derived, and comparison is made among the known bounds of Dennis [2], Döring [4], Gragg-Tapia [5], Kantorovich [6, 7], Kornstaedt [9], Lancaster [10], Miel [11–13], Moret [14], Ostrowski [17, 18], Potra [19], and Potra-Pták [20].This paper was written while the author was visiting the Mathematics Research Center, University of Wisconsin-Madison, U.S.A. from March 29, 1985 to October 21, 1985Sponsored by the Ministry of Education in Japan and the United States Army under Contract No. DAAG 29-80-C-0041     

An improved bound for the Minkowski dimension of Besicovitch sets in medium dimension

We use geometrical combinatorics arguments, including the "hairbrush" argument of Wolff [W1], the x-ray estimates in [W2], [LT], and the sticky/plany/grainy analysis of [KLT], to show that Besicovitch sets in have Minkowski dimension at least for all , where is an absolute constant depending only on n. This complements the results of [KLT], which established the same result for n = 3, and of [B3], [KT], which used arithmetic combinatorics techniques to establish the result for . Unlike the arguments in [KLT], [B3], [KT], our arguments will be purely geometric and do not require arithmetic combinatorics. Submitted: April 2000, Revised version: November 2000.