共查询到18条相似文献,搜索用时 93 毫秒
1.
引入实值函数关于有界闭凸值测度的集值积分,并讨论了集值积分的收敛定理,证明了当集值测度为有界闭凸集值的有界变差集值测度时,关于弱紧凸集值测度的积分性质对有界闭凸集值测度仍然保持.推广了实值函数关于弱紧凸值测度的积分. 相似文献
2.
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
3.
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
4.
给出集值Bartle积分一个新的定义,并进一步讨论了数值函数关于有界闭凸集值可数可加集值测度的积分的性质,建立了集值Bartle积分的新的极限定理. 相似文献
5.
6.
本文在可分自反Ranach空的的情形下,给出了任何一列两两等比、一致有界的矢值测度可以生成一个有界闭凸值集值测度的所谓表示定理,而这个定现对κ空间首先在[3]中建立。同时,找到了由一列两两等比、一致有界变差矢值测度所生成集值测度与这列矢值测度Radon-Nikodym导数之间的关系。 相似文献
7.
本文给出了集值映象的弱上半连续而非准上半连续的例子,证明了对于闭凸的集值映象弱上半连续和准上半连续等价,并把Kakutani不动点定理推广到非闭凸的弱上半连续的情形. 相似文献
8.
本文讨论了集值拟鞅和集值一致渐近鞅,证明了集值拟鞅与集值一致渐近鞅的选样定理,对于集值一致渐近鞅得到了一些收敛性结果,并由此刻化了空间的 Radon-Nikodym性质. 相似文献
9.
本文研究了离散参数集值序下鞅的Riesz分解及收敛性.利用集值序关系及集值鞅方法,给出了离散参数集值序下鞅的Riesz分解的存在性及唯一性定理.并获得离散参数集值序下鞅的收敛性定理. 相似文献
10.
周志昂 《数学的实践与认识》2007,37(15):131-135
我们讨论了广义次似凸集值优化的对偶定理.首先,我们给出了广义次似凸集值优化的对偶问题.其次,我们给出了广义次似凸集值优化的对偶定理.最后,我们考虑了广义次似凸集值优化问题的标量化对偶,并给出了一系列对偶定理. 相似文献
11.
Simeon Reich Alexander J. Zaslavski 《Journal of Fixed Point Theory and Applications》2013,13(2):627-632
It follows from Banach’s fixed point theorem that every nonexpansive self-mapping of a bounded, closed and convex set in a Banach space has approximate fixed points. This is no longer true, in general, if the set is unbounded. Nevertheless, as we show in the present paper, there exists an open and everywhere dense set in the space of all nonexpansive self-mappings of any closed and convex (not necessarily bounded) set in a Banach space (endowed with the natural metric of uniform convergence on bounded subsets) such that all its elements have approximate fixed points. 相似文献
12.
13.
We consider a general class of convex optimization problems in which one seeks to minimize a strongly convex function over a closed and convex set which is by itself an optimal set of another convex problem. We introduce a gradient-based method, called the minimal norm gradient method, for solving this class of problems, and establish the convergence of the sequence generated by the algorithm as well as a rate of convergence of the sequence of function values. The paper ends with several illustrating numerical examples. 相似文献
14.
M. Zohry 《Mathematische Nachrichten》2006,279(12):1376-1382
For an essentially bounded closed‐convex‐nonempty set‐valued random variable, it is shown that the conditional expectation is characterized by its integrals over the sets of the associated σ ‐field. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
15.
We obtain necessary conditions for the existence of fixed point and approximate fixed point of nonexpansive and asymptotically nonexpansive maps defined on a closed bounded convex subset of a uniformly convex complete metric space and study the structure of the set of fixed points. We construct Mann type iterative sequences in convex metric space and study its convergence. As a consequence of fixed point results, we prove best approximation results. We also prove Kantorovich-Rubinstein maximum principle in convex metric spaces. 相似文献
16.
S. Dancs P. Medvegyev Gy. Magyarkuti 《Journal of Optimization Theory and Applications》2011,150(3):675-682
The purpose of this short technical note is to show that a locally convex topological vector space is normable, if and only
if an important convergence theorem about closed and convex sets holds. This new assumption of normability is related to the
problem of preservation of Hausdorff lower continuity of the intersection of Hausdorff lower continuous, closed and convex
valued correspondences. 相似文献
17.
Nikolaos S Papageorgiou 《Proceedings Mathematical Sciences》1991,101(2):63-70
In this paper we prove some convergence theorems for Banach space valued multifunctions. First we consider the notion of weak
convergence of sets and prove a weak completeness and a weak compactness result of the Dunford-Pettis type for weakly compact,
convex valued integrable multifunctions. Then we consider set valued martingales and establish two convergence theorems. One
using the Kuratowski-Mosco mode of convergence and for the other the Hausdorff mode. 相似文献
18.
Károly Bezdek 《Israel Journal of Mathematics》1992,80(1-2):87-96
In this note we prove that the illumination of an almost bounded closed convex set by minimum number of affine subspaces of
given dimension can be reduced to the illumination of a bounded closed convex set of lower dimension.
The work was supported by Hung. Nat. Found. for Sci. Research No. 326-0213 相似文献