共查询到20条相似文献,搜索用时 62 毫秒
1.
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
2.
本文首先建立了实值非负函数关于集值序增函数的集值Riemann-Stieltjes积分,并讨论了集值Riemann-Stieltjes积分的性质,给出了集值Riemann-Stieltjes可积的充要条件,最后引入了集值Riemann-Stieltjes随机积分. 相似文献
3.
F.Hiai在集值测度有界变差的条件下,给出了Aumann积分的R-N性质,本文在集值测度为σ-有界变差的条件下,建立了集值测度表示成Pettis-Aumann积分的充要条件。 相似文献
4.
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
5.
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
6.
集值Lebesgue—Stieltjes积分 总被引:8,自引:2,他引:6
本文首先刻划了B(R_ )上的集值测度,其次建立了(R_ B(R_ ))上的集值Lebesgue-Stieltjes积分.最后,进—步建立了集值随机Lebesgue-Stietjes积分的理论. 相似文献
7.
8.
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
9.
吴健荣 《纯粹数学与应用数学》2001,17(4):370-376
对集值映射的Pettis-Aumann型积分的性质作了讨论,给出了Pettis-Aumann积分型积分的Fatou引理形式以及其它一些收敛定理,探讨了带参数集值映射的积分性质。 相似文献
10.
本文定义了一类有界可料过程关于集值平方可积鞅的集值随机积分,并研究了集植随机积分的性质。此为建立集值随机分析的理论奠定了基础。 相似文献
11.
集值Superpramart的上鞅逼近 总被引:6,自引:0,他引:6
李高明 《数学物理学报(A辑)》2000,20(2):163-168
文中讨论了可积随机集条件期望的若干性质,在此基础上给出了集值Superpramart的上鞅逼近,同时,证明了集值Superpramart 在Kuratowski-Mosco意义下的收敛定理。 相似文献
12.
In this article, by virtue of the Fan-Browder fixed point theorem, we first obtain a minimax theorem and establish an equivalent relationship between the minimax theorem and a cone saddle point theorem for scalar set-valued mappings. Then, by using scalarization functions, we investigate an existence theorem of the cone saddle point for set-valued mappings. Simultaneously, we also establish a minimax theorem for set-valued mappings. 相似文献
13.
《随机分析与应用》2013,31(2):401-418
We define a set-valued stochastic integral with respect to a 1-dimensional Brownian motion. The paper develops multivalued analogs to the theory of singlevalued stochastic integrals. It is expected that these results will be useful to study set-valued and fuzzy stochastic analysis. 相似文献
14.
《Optimization》2012,61(1):53-63
In this article, following the idea used by Göpfert et al . [A. Göpfert, Chr. Tammer and C. Zalinescu (2000). On the vectorial Ekeland's variational principle and minimal points in product spaces. Nonlinear Analysis, Theory, Methods & Applications , 39 , 909-922] to derive an Ekeland's variational principle for vector-valued functions, we derive a new variant of Ekeland's variational principle for set-valued maps. Finally, we apply this variational principle to obtain an approximate necessary optimality condition for a class of set-valued optimization problems. 相似文献
15.
Chen G. Y. Huang X. X. Hou S. H. 《Journal of Optimization Theory and Applications》2000,106(1):151-164
In this paper, we introduce the concept of approximate solutions for set-valued optimization problems. A sufficient condition for the existence of approximate solutions is obtained. A general Ekeland's variational principle for set-valued mappings in complete ordered metric spaces and complete metric spaces are derived. These results are generalizations of results for vector-valued functions in Refs. 1–4. 相似文献
16.
Andreas H. Hamel 《Set-Valued and Variational Analysis》2009,17(2):153-182
It is proven that a proper closed convex function with values in the power set of a preordered, separated locally convex space
is the pointwise supremum of its set-valued affine minorants. A new concept of Legendre–Fenchel conjugates for set-valued
functions is introduced and a Moreau–Fenchel theorem is proven. Examples and applications are given, among them a dual representation
theorem for set-valued convex risk measures.
相似文献
17.
锥凸集值映射的基本性质 总被引:3,自引:0,他引:3
本文首先在R~m的幂集上定义了一种锥序关系并借助这种序关系定义锥凸集值映射,证明了普通单值凸函数的一些基本性质拓广到这种锥凸集值映射时仍成立. 相似文献
18.
S. K. Mishra S. Y. Wang K. K. Lai 《Journal of Optimization Theory and Applications》2008,138(1):77-84
Variational-like inequalities with set-valued mappings are very useful in economics and nonsmooth optimization problems. In
this paper, we study the existence of solutions and the formulation of solution methods for vector variational-like inequalities
(VVLI) with set-valued mappings. We introduce gap functions and establish necessary and sufficient conditions for the existence
of a solution of the VVLI. We investigate the existence of a solution for the generalized VVLI with a set-valued mapping by
exploiting the existence of a solution of the VVLI with a single-valued function and a continuous selection theorem.
The research of first author was partially supported by the Council of Scientific and Industrial Research, New Delhi, Ministry
of Human Resources Development, Government of India Grant 25(0132)/ER-II/2004. 相似文献
19.
本文利用集值映射弱次梯度的Morea-Rockafellar定理,在内部(锥)-凸性假设下,得到了集值映射关于Henig有效性的Morea-Rockafellar定理.其结论为:在内部(锥)-凸条件下,两个集值映射和的Henig有效次梯度可以表示成它们Henig有效次梯度的和. 相似文献
20.
M. Durea 《Journal of Optimization Theory and Applications》2007,133(1):111-116
In this note, we derive first and second-order necessary (resp. sufficient) conditions for local minimum (resp. strict local
minimum) points of optimization problems governed by set-valued maps. This allows us to present and to solve a generalized
Lagrange claim in a multivalued setting. 相似文献