增生算子的非线性方程的逼近法

设X是一致凸且一致光滑的实Banach空间,T:D(T),X"X是定义域为闭集D(T),值域为有界集R(T)的m-增生算子,本文证明了Ishikawa迭代强收敛到方程x+Tx=f的唯一解。     

集值渐近准非扩张映象多步迭代的收敛性

在严格凸Banach空间中,用集值映象点值化方法,证明了集值渐近准非扩张映象带误差的三步迭代列收敛于耦合不动点的充要条件.     

关于带误差的Ishikawa迭代过程

在一致凸Banach空间中研究了非扩张映射序列的带误差Ishikawa迭代过程的构造和收敛问题,推广了近期的结果。     

非扩张型映象的近似耦合不动点与耦合不动点定理

在具有Opial条件的Banach空间中获得了非扩张映象的近似耦合不动点和耦合不动点存在定理.     

一类经典Banach格上保不交算子的矩阵刻画

对向量格Rn 到Rm 的保不交算子进行矩阵刻画 ,即矩阵的每行至多有一个元素不为零 .并把此结果推广到了经典Banach格c0 和lp(1≤p <∞ )到l∞(c或c0 )的有界保不交算子的情况 .讨论了具有不交Schauder基的Banach格上有界保不交算子的矩阵特征 .     

Iterative Processes with Errors for Generalized Set-Valued φ-Hemi-contractive Mapping in Banach Spaces

Introduction Variational inequality is one of the most interest-ing and important mathematical problems and hasbeen studied intensively in the past years since theyhave wide applications to mechanics, physics, opti-mization and control, nonlinear programm…     

任意Banach空间强伪压缩映射不动点的迭代逼近

利用正规对偶映射的定义，给出了任意Banach空间Lipschitz强伪压缩映射不动点的Ishikawa迭代收敛定理。该定理不仅推广了已知结果，而且还简化了目前相应结果的证明。     

On the realization of nonlinear wave profiles using the Banach fixed-point theorem: Stokes wave in a finite depth

A new mathematical formulation for the realization of nonlinear wave profiles and its nonlinear solution procedure, based on the Banach fixed-point theorem, is proposed. To apply the formulation, a nonlinear equation for the Stokes wave in a finite depth was derived, and some numerical solutions are given. A numerical study showed that the proposed iteration method, based on linear progressive wave potential only, enabled us to realize the Stokes nonlinear wave profiles in a finite depth. The nonlinear strategy of iteration has a very fast convergence rate, i.e., only about 6–10 iterations are required to obtain a numerically converged solution.     

Banach空间中非扩张映射的不动点逼近的Ishikawa迭代程序

设X为实一致凸Banach空间,其共轭空间X*具有KK性质,C为X的非空有界闭凸子集。若T为C到自身的非扩张映射,则对任给的x0∈C,Ishikawa迭代程序xn 1=tnT(snTxn (1-sn)xn) (1-tn)xn,n=0,1,2,…,定义的序列{xn}弱收敛到T的某个不动点,其中{tn},{sn}满足一定的条件。     

Some Remarks on Operators and Their Conjugates

We first characterize the range spaces F for which {T':T∈K(E,F)}=K(F',E') holds for all Banach spaces E. Then we present some sufficient conditions for the equality T'=T'. Some related results are also included.