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1.
集值增过程产生的集值测度   总被引:2,自引:0,他引:2  
本文首先研究集值增函数在B(R+)上产生的集值测度,然后在其基础上研究集值增过程A(ω,t),(ω,t)∈Ω×R+,在乘积可测空间F×B(R+)上产生的集值测度,在一定条件下建立了两者之间的一一对应关系.  相似文献   

2.
设X是可分自反Banach空间,(F,A,t∈R+)是取值于X中闭凸集的可测集值随机过程,该文证明了,若任给停时T,FTI(T〈∞)关于AT(相应地关于A)是σ一可积,则(F,t∈R+)必存在可选(相应地可料)投影过程。  相似文献   

3.
本文引入了集值马尔可夫过程的可测同构选择算子,并用它解决了一类集值马尔可夫过程的可测选择问题.  相似文献   

4.
本文在研究了在非空有界闭紧凸集空间中适应可积集值函数列的收敛性,引入正向集值mil的基础上,利用可测分割法,得到了收敛性定理及其证明.  相似文献   

5.
首先给出有界闭凸集值序增函数以及有界闭凸集序增过程的定义;然后讨论了有界闭凸集值序增函数以及有界闭凸集值序增过程的性质.  相似文献   

6.
在[2]、[3]给出的正则F集度量拓扑的基础上,以Borel可测的形式定义了论域为R^n的Fuzzy值可测函数,并证明了该可测函数定义与水平可测定义^[1-4]的等价性.从而为Fuzzy值可测函数的进一步研究提供了一条新的途径。  相似文献   

7.
吴健荣  吴从炘 《数学学报》2001,44(2):249-258
本文建立了 Banach空间集值测度的 Radon-Nikodym定理,并给出了两类集值算子的Pettis-Aumann积分表示.  相似文献   

8.
本文建立了 Banach空间集值测度的 Radon-Nikodym定理,并给出了两类集值算子的Pettis-Aumann积分表示.  相似文献   

9.
Pettis-Aumann积分的若干性质   总被引:1,自引:0,他引:1  
薛小平  陈兵 《应用数学》1993,6(2):219-221
自文[1]建立了R~n空间的集值映射积分以来,讨论集值映射的可测性、可测选择、集值条件概率、鞅及其Radon-Nikodym定理等方面的工作相继出现.文[6]又系统地研究了R~n空间中集值测度的凸性定理、选择性定理以及与Aumann积分的关系.文[7]则讨论了集值测度的生成定理.但讨论Pettis-Aumann积分的工作目前尚未见到.  相似文献   

10.
本文庆可分自反Banach空间的情况下,得到了集值映射可由Aumann积分表示的充要条件。  相似文献   

11.
Summary An existence result of strongly measurable selection of a weakly measurable multifunction from a compact space with non empty convex weakly compact values in a Banach space is given. Some compactness results concerning the set of integrable selections of a weakly measurable multifunction with non empty convex weakly compact values in a weakly compact set of a Banach space and the multivalued integral of such multifunction are presented.  相似文献   

12.
The Cauchy problemdu/dt+Au+B(t,u)∋0,u(0)=u 0 is studied in a separable Hilbert space setting, whenA is a multivalued maximal monotone operator, andB is a multivalued operator which is measurable with respect to the time variable and upper semi-continuous with respect to the space variable. Under some boundedness conditions onB, an existence theorem is proved, with the extra assumption, in the infinite dimensional case thatA is the subdifferential of a proper lower semi-continuous inf-compact convex function. A theorem of dependence upon the initial condition is also given.  相似文献   

13.
《Quaestiones Mathematicae》2013,36(4):503-512
A multivalued linear projection operator P defined on linear space X is a multivalued linear operator which is idempotent and has invariant domain. We show that a multivalued projection can be characterised in terms of a pair of subspaces and then establish that the class of multivalued linear projections is closed under taking adjoints and closures. We apply the characterisations of the adjoint and completion of a projection together with the closed graph and closed range theorems to give criteria for the continuity of a projection defined on a normed linear space. A new proof of the theorem on closed sums of closed subspaces in a Banach space (cf. Mennicken and Sagraloff [9, 10]) follows as a simple corollary. We then show that the topological decomposition of a space may be expressed in terms of multivalued projections. The paper is concluded with an application to multivalued semi-Fredholm relations with generalised inverses.  相似文献   

14.
In this paper, we introduce a new one-step iterative process to approximate the common fixed points of two multivalued nonexpansive mappings. We will also prove a strong convergence theorem in a uniformly convex Banach space under the multivalued version of so-called Condition (A′).  相似文献   

15.
The present paper is a survey of the contemporary state of art in the theory of multivalued mappings. In it one considers different forms of continuity of multivalued mappings, one investigates differentiable and measurable multivalued mappings, one considers single-valued continuous approximations and sections of multivalued mappings, one studies fixed points of multivalued mappings and other questions of this theory. One gives references to the literature regarding applications to the theory of games, mathematical economics, the theory of differential inclusions and generalized dynamical systems. The paper contains an extensive bibliography.Translated from Itogi Nauki i Tekhniki, Seriya Matematicheskii Analiz, Vol. 19, pp. 127–230, 1982.  相似文献   

16.
一类多值算子方程的迭代算法   总被引:1,自引:0,他引:1  
本讨论Hilbert空间上具有强单调、上半Lipschitz连续性质的多值算子方程的求解方法,构造了迭代格式并证明迭代过程是收敛的;同时给出它在求解多值微分方程边值问题中的应用。  相似文献   

17.
We establish △-convergence and strong convergence theorems for an iterative process for a finite family of generalized nonexpansive multivalued mappings in a CAT(0) space. Moreover, we present a fixed point theorem for a pair consisting of a finite family of generalized nonexpansive single valued mappings, and a generalized nonexpansive multivalued mapping in CAT(0) spaces.  相似文献   

18.
In this article we state conditions under which the existence of deterministic coincidence points of two multivalued random functions implies the existence of random coincidence points. Moreover, two existence results of measurable selections are obtained for the intersection of the multivalued function evaluated at the random coincidence point. Our results extend or improve some theorems in the literature.  相似文献   

19.
In this paper, we introduce a new one-step iterative process to approximate common fixed points of two multivalued nonexpansive mappings in a real uniformly convex Banach space. We establish weak and strong convergence theorems for the proposed process under some basic boundary conditions.  相似文献   

20.
在Banach中讨论了一类二阶微分包含的边值问题和一类反馈控制问题.结合不动点定理,对解的存在性给出了两个充分性条件,最后应用前面的结果建立了反馈控制问题解的存在性定理.  相似文献   

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