Ou-Iang积分不等式的推广

本文推广了Ｏｕ－Ｉａｎｇ在文［１］中给出的一类积分不等式     

关于n个无关变元的欧阳型离散型不等式

本文讨论关于ｎ个无关变元的Ｏｕ－Ｉａｎｇ型离散型不等式，所得结论是杨恩浩的Ｎ１上的Ｏｕ－Ｉａｎｇ型离散型不等式的自然推广和改进．     

模糊值函数与模糊数积分区间[A,B]上的N—L公式

文「１」给出模糊值函数在普通区间「ａ,ｂ」上的Ｎ－Ｌ公式。本文在文「１」的基础上进一步给出模糊值函数区间「Ａ,Ｂ」上的积分。这个积分是Ⅱ型糊集。文「３」已经指出（Ｆ２「１,１」,∪,∩,ｃ）不是软代数,但这个积分是一个特殊Ⅱ型模糊集具有许多良好的代数性质,并存在着Ｎ－Ｌ公式。     

Musielak—Orlicz序列空间的光滑性质

本文给出了Ｍｕｓｉｅｌａｋ－Ｏｒｌｉｅｚ序列空间简洁的光滑点判据,从而得到十分便于应用的空间光滑性判别条件,同时纠正了「１」中主要定理的错误。     

神经传播型方程初值问题解的Blow—up

在「１」的基础上进一步研究神经传播型方程的初值问题解的非整体存在性与ｂｌｏｗ－ｕｐ。通过引进一归一化的高斯函数作为初值问题“特征函数”证明了，当ｆ（ｕ），ｇ（ｕ）与初值「１」类的条件时，解在有限时间为ｂｌｏｗ－ｕｐ，从而推广和衩了「１」的结果。     

关于一类交换子的加权不等式

本文考虑了带有仿Ｌ＾ｑ－Ｄｉｎｉ奇异积分核的卷积算子的交换子的加权不等式，得到两个主要结果，从而在某种意义上推广了Ｓｔｅｖｅｎ Ｂｌｏｏｍ「２」的结果。     

类似Hilbert不等式的一些新不等式的推广

本文推广了Ｐａｃｈｐａｔｔｅ在文「１」中给出的类似Ｈｉｌｂｅｒｔ不等式的一些新不等式。     

关于Γ-除环

文中首先给出了定理２．２,由它可以行到文献「４」和「５」中关于Γ－域和除Γ－环的一些结果,其次,我们还指出了一个Γ－环是Γ－除环的几个条件。     

关于M—矩阵等价表征的注记

「２」指出了「１」的某些错误,并给出了修正的结果。本继续「２」的讨论,给出了Ｍ－矩阵等价表征的进一步结果。     

关于∑*-空间的一点注记

指出Ｄｎ真包含于∪｛Ｅｍ：ｍ∈Ｎ｝对σ－空间成立,但对∑＾＊－空间,我们给出了一个例子说明它是不成立的。因而「５」中是３．２．１３是不对的。这样「３」中的主要结论需要重新考虑。     

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].     

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].     

亚纯函数微分多项式f~kQ[f]+P[f]的零点分布

文[4]对简单形式的微分多项式fkf’+a的零点分布进行了讨论,文[1]对一般形式的微分多项式fkQ[f]+P[f]的零点分布进行了讨论.但由于极点给证明带来的困难,这些工作主要是对整函数来做的.本文证明了任一满足δ(∞,f)>k+2ΓQ+3ΓP+2/2k+2ΓQ+1的超越亚纯函数f,微分多项式fkQ[f]+P[f]在不含f,Q[f]极点和P[f]零、极点的可数个圆盘并集之外有无穷多个零点,其中k≥3Γp+2,而ΓQ,ΓP分别是f的微分多项式Q[f],P[f]的权.文[1]和[2,4,6]中的结论是本文结论的特殊情况.     

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.     

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.     

Hardy-Hilbert重级数不等式的推广与改进

本文将著名的 Hardy-Hilbert重级数不等式∑∞m=1 ∑∞n=1ambnm + n≤ πsin(π/p) ∑∞n=1apn1p ∑∞n=1bqn1q∑∞m=1 ∑∞n=1anm + np ≤ πsin(π/p)p∑∞n=1apn进行了带参数形式的推广 ,同时改进了这些不等式     

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].     

Niveau hermitien de Certaines algèbres de quaternions

Let D [d] =(a,b/F) a quaternion divisior algebra over a field F of characteristic ? 2. Denote 1, i, j , k the basis of D, such that i²[d] n, j²[d] b, ij [d] -ji [d] k and A :D → D the involution given by i [d] -i, j [d] j (and k [d] k). In [LE] D. LEWIS asks the following question :Does there exist a quadratic Pfister form [S p. 721 [d] such that the hermitian form [d] [d] D is isotropic over (D, [d]) but not hyperbolic &; In this note, we show that the answer of this question is negative, so that the hermitien level [§I], when it is finite, of (D, A) is a power of two. This result holds for quaternion algebras with standard involution [LE].     

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.