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1.
首先证明了Frechet光滑Banach空间上齐次函数的次微分的一个有用定理,然后利用下半连续函数和的次微分规则把Clarke-Ledyaev多方向中值不等式推广到多个函数的情形.  相似文献   

2.
关于Banach空间中凸泛函的广义次梯度不等式   总被引:2,自引:0,他引:2  
姚云飞  徐森林 《应用数学》2003,16(3):136-140
本文在前人^[1,2]的基础之上,以凸泛函的次梯度不等式为工具,将Jensen不等式推广到Banach空间中的凸泛函,导出了Banach空间中的Bochner积分型的广义Jensen不等式,给出其在Banach空间概率论中某些应用,从而推广了文献[3—6]的工作.  相似文献   

3.
鞅型序列与FRECHET空间的核性   总被引:1,自引:1,他引:0  
如所周知,向量值鞅和渐近鞅是研究空间性质的有力工具。特别地,在文献[1]-[6]中,L.Egghe与A.Bellow等利用渐近鞅的有关性质分别刻划了Banach空间的有限维特征和Frechet空间的核性特征。本文进一步研究鞅型序列的性质,得到了Frechet空间具有核性的另一些等价条件,给出了鞅型序列的分解定理和收敛定理,推广了上述文献中的有关结果。  相似文献   

4.
在具Frechet可微范数的一致凸Banach空间中,给出了渐近非扩张拓扑半群的遍历压缩定理  相似文献   

5.
利用粘性逼近方法,在自反Banach空间的框架下,研究无限族非扩张映象及对给定的压缩映象的迭代程序的收敛性问题.在适当的条件下,证明了该迭代序列强收敛于某一公共不动点,而且这一公共不动点也是自反Banach空间中某一变分不等式的唯一解.所得结果改进和推广了一些人的最新的结果.  相似文献   

6.
本文引进了一个集族O_(?),用它把Kato的方法推广到了局部凸的拓扑线性空间,得到了某些半序Frechet空间中生成一个正半群的充要条件,把这些条件用到半序Banach空间上时,可以得到一些新结果,同时,把Kato的定理推广到了局部凸拓扑线性空间。  相似文献   

7.
该文首先研究吸引非扩张映射的性质,然后在一致光滑Banach空间里,用这些性质研究两个非扩张映射的不动点问题的粘性迭代算法.作为应用,在Banach空间或Hilbert空间里,得到了关于变分不等式问题,不动点问题和均衡问题的强收敛定理.所得结果提高和推广了许多最近的相关结果.  相似文献   

8.
本文将Cn中的Roper-Suffridge算子推广到任意复Banach空间中,并证明这种算子在任意复Banach空间中的某些区域上具有保持ε星形性,由此可以构造出任意复Banach空间,复Hilbert空间和Cn中的一些区域上的许多双全纯星形映照、双全纯凸映照、双全纯ε星形映照,同时,得到它们的增长定理等,将龚升与刘太顺,Roper与suffridge,Graham,Kohr等学者在Cn中的一些结果推广到任意复Banach空间或复Hilbert空间中.  相似文献   

9.
Banach值鞅变换算子的有界性   总被引:7,自引:0,他引:7  
翟富菊  张传洲 《数学杂志》2004,24(3):341-346
本文运用Banach值鞅不等式和鞅空间的相互嵌入关系.讨论了Banach空间值鞅空间上鞅变换算子L的有界性.并给出了鞅变换算子的有界性与Banach空间几何性质的关系.  相似文献   

10.
B值行独立随机元阵列的完全收敛性   总被引:1,自引:0,他引:1  
邱德华  甘师信 《数学杂志》2005,25(2):225-230
本文研究了B值行独立的随机元阵列完全收敛性,在对Banach空间B没有p型的要求下,根据Banach空间上的A.de Acosta.不等式与Hoffman-JФrgensen不等式,得到了几个有意义的结果.  相似文献   

11.
In this paper, we discuss isotonicity characterizations of the metric projection operator, including its necessary and sufficient conditions for isotonicity onto sublattices in Banach spaces. Then, we demonstrate their applications to variational inequalities and fixed point theory in Banach spaces. Our work generalizes many existing results obtained in earlier work.  相似文献   

12.
Banach空间的p— Asplund 伴随空间   总被引:4,自引:1,他引:3  
我们称一个定义在Banach空间E上的连续凸函数f具有Frechet可微性质(FDP),如果E上的每个实值凸函数g≤f均在E一个稠密的Gδ-子集上Frechet可微。本文主要证明了:对任何Banach空间E,均存在一个局部凸相容拓扑p使得1)(E,p)是Hausdorff局部凸空间;2) E上的每个范数连续具有FDP的凸函数均是p-连续的;3)每个p-连续的凸函数均具有FDP ;4)p等价某个范数拓扑当且仅不E是Asplund空间。  相似文献   

13.
In this paper the operator-valued martingale transform inequalities in rearrangement invariant function spaces are proved. Some well-known results are generalized and unified. Applications are given to classical operators such as the maximal operator and the p-variation operator of vector-valued martingales, then we can very easily obtain some new vector-valued martingale inequalities in rearrangement invariant function spaces. These inequalities are closely related to both the geometrical properties of the underlying Banach spaces and the Boyd indices of the rearrangement invariant function spaces. Finally we give an equivalent characterization of UMD Banach lattices, and also prove the Fefferman-Stein theorem in the rearrangement invariant function spaces setting.  相似文献   

14.
Banach空间中非Lipschitzian交换非线性拓扑半群的遍历理论   总被引:3,自引:0,他引:3  
李刚  马吉溥 《数学学报》1997,40(2):191-201
本文在满足opial条件或存在Frechet可微范数的一致凸Banach空间中,给出了非Lipschitzian交换拓扑半群的遍历收敛定理及弱收敛定理.  相似文献   

15.
Existence results for systems of vector variational-like inequalities   总被引:1,自引:0,他引:1  
The purpose of this paper is to introduce and study systems of vector variational-like inequalities in Banach spaces. Under certain conditions, some existence results for systems of vector variational-like inequalities in Banach spaces are obtained by Kakutani–Fan–Glicksberg fixed point theorem.  相似文献   

16.
We present a characterization of the completed Borel measure spaces for which every measurable function, with values in a separable Frechet space, is the almost everywhere limit of a sequence of continuous functions. From this characterization one can easily obtain results that have appeared recently in the literature, in a more general form. We also examine what happens when the range is a subset of an arbitrary Banach space, and show that this case often reduces to the separable case.  相似文献   

17.
We develop a generalized differentiation theory for nonsmooth functions and sets with nonsmooth boundaries defined in Asplund spaces. This broad subclass of Banach spaces provides a convenient framework for many important applications to optimization, sensitivity, variational inequalities, etc. Our basic normal and subdifferential constructions are related to sequential weak-star limits of Fréchet normals and subdifferentials. Using a variational approach, we establish a rich calculus for these nonconvex limiting objects which turn out to be minimal among other set-valued differential constructions with natural properties. The results obtained provide new developments in infinite dimensional nonsmooth analysis and have useful applications to optimization and the geometry of Banach spaces.

  相似文献   


18.
We shall present several Hanner type inequalities with a weight constant and characterize 2-uniformly smooth and 2-uniformly convex Banach spaces with these inequalities. p-Uniformly smooth and q-uniformly convex Banach spaces will be also characterized with another Hanner type inequalities with a weight in the other side term. The best value of the weight in these inequalities will be determined for Lp spaces. Also we shall present a duality theorem between these inequalities in a generalized form.  相似文献   

19.
We establish inequalities between entropy numbers and approximation numbers for operators acting between Banach spaces. Furthermore we derive inequalities between eigenvalues and entropy numbers for operators acting on a Banach space. The results are compared with the classical inequalities of Bernstein and Jackson.  相似文献   

20.
研究了半序Banach空间中一类非线性锥映射歧点的存在性与正特征元的全局结构.与已知文献不同的是,不要求算子在零点沿着锥Frechet可微. 作为应用,讨论了一类椭圆型偏微分方程边值问题正解的歧点与全局结构.  相似文献   

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