共查询到19条相似文献,搜索用时 109 毫秒
1.
非线性Lipschitz算子的Lipschitz对偶算子及其应用 总被引:3,自引:0,他引:3
在文山中我们对非线性Lipschitz算子定义了其Lipschitz对偶算子,并证明了任意非线性Lipschitz算子的Lipschitz对偶算子是一个定义在Lipschitz对偶空间上的有界线性算子.本文还进一步证明:设C为 Banach空间 X的闭子集,C*L为C的 Lipschitz对偶空间,U为 C*L上的有界线性算子,则当且仅当 U为 w*-w*连续的同态变换时,存在Lipschitz连续算子T,使U为T的Lipschitz对偶算子.这一结论的理论意义在于:它表明一个非线性Lipschitz算子的可逆性问题可转化为有界线性算子的可逆性问题.作为应用,通过引入一个新概念──PX-对偶算子,在一般框架下给出了非线性算子半群的生成定理. 相似文献
2.
齐型空间上的Lipschitz函数与Littlewood-Paley g-函数 总被引:1,自引:0,他引:1
在θ阶正规齐型空间上,如果算子列{Sk}k∈Z是恒等逼近,Dk=Sk-Sk-1;本文给出一个用{Dk}k∈Z表达的f∈Lipα(Lipschitz函数类,0<α<θ)的充分必要条件.作为其推论得到,对于f∈LIpα,其Littlewood-Paleyg函数g(f)(X)或者处处为无穷大,或者在Lipα上有界. 相似文献
3.
齐型空间上的Lipschitz函数与Littlewood-Paley g-函数 总被引:3,自引:0,他引:3
在θ阶正规齐型空间上,如果算子列{Sk}k∈Z是恒等逼近,Dk=Sk-Sk-1;本文给出一个用{Dk}k∈Z表达的f∈Lipα(Lipschitz函数类,0<α<θ)的充分必要条件.作为其推论得到,对于f∈LIpα,其Littlewood-Paleyg函数g(f)(X)或者处处为无穷大,或者在Lipα上有界. 相似文献
4.
一类广义Lipschitz非线性算子的带误差的Ishikawa迭代程序 总被引:33,自引:0,他引:33
借助于周海云和陈东青[4]新近引入的广义Lipschitz概念,研究了实Banach空间中广义Lipschitz -强伪压缩算子的不动点和广义Lipschitz -强增算子方程解的迭代逼近问题,所得结果改进和扩展了近期许多相关的结果,并部分地回答了周海云[3]提出的一个问题. 相似文献
5.
Lipschitz-α算子的M-谱理论 总被引:6,自引:0,他引:6
本文运用一个选定的可逆Lip-α算子M作为尺度算子(称为谱尺度),引入两个Banach空间之间的非线性Lip-α算子的M-豫解集、M-谱集、M-谱半径、豫解集、谱集及谱半径,证明了它们的一列系重要性质,给出了M-谱的一个摄动定理,初步建立了Lip-α算子的M-谱理论,使得现有的谱理论成为其特例. 相似文献
6.
Szasz型算子同时逼近的点态结果 总被引:3,自引:1,他引:2
本文给出了Szasz-irakjan算子和Szasz-Kantorovich算子组合的同时逼近的点态结果,并用其导数给出了高阶Lipschitz函数类的特征刻划。 相似文献
7.
8.
杨长森 《数学物理学报(A辑)》1996,16(1):69-75
该文主要给出了经典的Marcinkiewicz-zygmund定理在2-型Banach空间中仍有其表现形式,并且指出它可到研究某些算子值随机元列。 相似文献
9.
杨长森 《数学物理学报(A辑)》1996,(1)
该文主要给出了经典的Marcinkiewicz-zygmund定理在2-型Banach空间中仍有其表现形式,并且指出它可应用到研究某些算子值随机元列. 相似文献
10.
本文证明,对于Lipschitz空间Lipα(Rn)的函数f,若相应Littlewood-Paley的g函数的g(f)(x)(或面积函数S(f)(x))在Rn中一点有限,则它必处处有限,并且作为Lipα(Rn)上的算子,g和S在一定意义下有界,这对一切α,0<α<1,和适当的λ成立. 相似文献
11.
Etienne Emmrich 《Numerical Functional Analysis & Optimization》2013,34(5-6):486-498
Based on an external approximation scheme for the underlying Banach space, a nonlinear operator equation is approximated by a sequence of coercive problems. The equation is supposed to be governed by the sum of two nonlinear operators acting between a reflexive Banach space and its dual. Under suitable stability assumptions and if the underlying operators can be approximated consistently, weak convergence of a subsequence of approximate solutions is shown. This also proves existence of solutions to the original equation. 相似文献
12.
Banach空间的Lipschitz对偶及其应用 总被引:3,自引:0,他引:3
本文引进Banach空间E的一个全新对偶空间概念—Lipschitz对偶空间,并证明:任何Banach空间的Lipschitz对偶空间是某个包含E的Banach空间的线性对偶空间,以所引进的新对偶空间为框架,本文定义了非线性Lipschitz算子的Lipshitz对偶算子,证明:任何非线性Lipschitz算子的Lipschitz对偶算子是有界线性算子.所获结果为推广线性算子理论到非线性情形(特别,运用线性算子理论研究非线性算子的特性)开辟了一条新的途径.作为例证,我们应用所建立的理论证明了若干新的非线性一致Lipschitz映象遍历收敛性定理. 相似文献
13.
Ju Myung Kim 《Journal of Mathematical Analysis and Applications》2007,327(1):257-268
This paper is concerned with the space of all compact adjoint operators from dual spaces of Banach spaces into dual spaces of Banach spaces and approximation properties. For some topology on the space of all bounded linear operators from separable dual spaces of Banach spaces into dual spaces of Banach spaces, it is shown that if a bounded linear operator is approximated by a net of compact adjoint operators, then the operator can be approximated by a sequence of compact adjoint operators whose operator norms are less than or equal to the operator norm of the operator. Also we obtain applications of the theory and, in particular, apply the theory to approximation properties. 相似文献
14.
We show that the lower limit of a sequence of maximal monotone operators on a reflexive Banach space is a representable monotone
operator. As a consequence, we obtain that the variational sum of maximal monotone operators and the variational composition
of a maximal monotone operator with a linear continuous operator are both representable monotone operators. 相似文献
15.
Xing-Hua ZhuJian-Zhong Xiao 《Applied mathematics and computation》2011,217(12):6004-6010
A new continuity theorem of minimum selection is presented for a continuous set-valued operator from a topological space into a Banach space with some uniform convexity. As applications, some problems concerning minimum right inverses for linear operators and minimum fixed points for condensing set-valued nonlinear operators are discussed. Also, the existence of minimum solutions for an integral inclusion is proved. 相似文献
16.
We consider a new class of narrow orthogonally additive operators in lattice-normed spaces and prove the narrowness of every C-compact norm-laterally-continuous orthogonally additive operator from a Banach–Kantorovich space V into a Banach space Y. Furthermore, every dominated Urysohn operator from V into a Banach sequence lattice Y is also narrow. We establish that the order narrowness of a dominated Urysohn operator from a Banach–Kantorovich space V into a Banach space with mixed norm W implies the order narrowness of the least dominant of the operator. 相似文献
17.
迭代逼近m-增生映象的零点 总被引:2,自引:0,他引:2
设E是具有一致正规结构的实Banach空间,其范数是一致Gateaux可微的.设A是m-增生映象,使得C=■是E的凸子集,数列{α_n)■[0,1],{r_n}■ (0,∞),在适当的条件下,则由(1.2)式定义的迭代序列{x_n}强收敛于A~(-1)(0)中的点.其次证明了:设E是一致凸Banach空间,其范数是Frechet可微的.设数列{α_n},{β_n)■(0,1),{r_n}■(0,∞),满足适当的条件.如果A~(-1)(0)∩B~(-1)(0)≠φ,则由(3.20)式定义的序列{x_n}弱收敛于A~(-1)(0)∩B~(-1)(0)中的点.其结果推广和改进了Kamimura,Takahashi(2000)的定理2及Xu H.K.(2006)的定理4.1,定理4.2和定理4.3:(i)Kamimura,Takahashi(2000)定理2中的假设"自反Banach空间E的每个有界闭凸子集对非扩张自映象有不动点性质"被去掉;(ii)Xu H.K.(2006)的假设"E是具有弱连续对偶映象J_φ的自反Banach空间",被本文的假设"E是具有一致正规结构且其范数是一致Gateaux可微的Banach空间"所取代.从而补充了Xu H.K.(2006)未包含的另外一些Banach空间.同时还证明了逼近两个m-增生映象的公共零点,其结果也推广和改进了Mainge的相应结果. 相似文献
18.
Dariusz Bugajewski Xiao-Xiong Gan Piotr Kasprzak 《Nonlinear Analysis: Theory, Methods & Applications》2012
In the first part of the paper we examine mappings of higher order from a general point of view, that is, in normed spaces of bounded real-valued functions defined on R. Particular attention is paid to the relation of such mappings with the so-called autonomous superposition operators. Next we investigate mappings of higher order in Banach spaces of almost periodic functions and their perturbations. We also give necessary and sufficient conditions guaranteeing that a nonautonomous superposition operator acts in the space of almost periodic functions in the sense of Levitan and is uniformly continuous. In the Banach space of bounded almost periodic functions in the sense of Levitan we discuss mappings of higher order and a convolution operator. Some applications to nonlinear differential and integral equations are given. 相似文献