共查询到20条相似文献,搜索用时 69 毫秒
1.
本文对J.-P.Aubin与H.Frankowska最近关于自反严格凸Banach空间中闭凸集值映射最小选择连续的于个结果加以讨论,首先在比自反性较强的一类空间中讨论了在弱ubin与H.Frankowska的条件下闭凸集值映射最小选择的连续性,其次对J.P.Aubin与H.Frankowska的结果给出了一个新的简单证明,最后用反例说明本文给出的条件J.P.Aubin与H.Frankowsaka条 相似文献
2.
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
3.
黄辉 《高校应用数学学报(A辑)》2007,22(1):74-80
考虑了伪凸集值映射的误差界.证明了对于伪凸集值映射,局部误差界成立意味着整体误差界成立.通过相依导数,给出了伪凸集值映射存在误差界的一些等价叙述. 相似文献
4.
黄辉 《高校应用数学学报(A辑)》2003,18(3):357-364
考虑了凸集值映射的整体误差界,推广Li和Singer(1998)的主要定理到无界情形并肯定地回答了该文的猜想.作为应用,给出了线性Hoffman误差界定理一个简单的新证明. 相似文献
5.
6.
7.
8.
本文首先在赋范线性空间中引入一类广义强凸集值映射,称之为h-强凸集值映射.其次利用R?dstr?m消去律研究了h-强凸集值映射的一些基本性质.最后,给出h-强凸集值映射形式下赋范线性空间为内积空间的刻画条件. 相似文献
9.
给出图闭模糊映射和闭模糊映射的关系:图闭模糊映射一定是闭模糊映射;若闭模糊映射是上半连续的则它也是图闭模糊映射. 相似文献
10.
11.
D. B. Rokhlin 《Mathematical Notes》2007,81(3-4):543-548
For set-valued random sequences (G n) n=0 N with relatively open convex values G n(ω), we prove a new test for the existence of a sequence (x n) n=0 N of selectors adapted to the filtration and admitting an equivalent martingale measure. The statement is formulated in terms of the supports of regular upper conditional distributions of G n. This is a strengthening of the main result proved in our previous paper [1], where the openness of the set G n(ω) was assumed and a possible weakening of this condition was discussed. 相似文献
12.
《Optimization》2012,61(6):763-780
The notion of covering is introduced for a set-valued mapping defined on an arbitrary set in a Banach space. A necessary and sufficient covering criterion is proved. The conditions are formulated in terms of generalized differentials and generalized normals. The covering theorem is applied to deduce formulas of generalized differential calculus and necessary optimality conditions for nonsroooth optimization problems. 相似文献
13.
Given a nonempty convex set X in a locally convex Hausdorff topological vector space, a nonempty set Y and two set-valued mappings T: X ? X, S: Y ? X we prove that under suitable conditions one can find an x ∈ X which is simultaneously a fixed point for T and a common point for the family of values of S. Applying our intersection theorem, we establish a common fixed point theorem, a saddle point theorem, as well as existence results for the solutions of some equilibrium and complementarity problems. 相似文献
14.
A. Ioffe 《Journal of Mathematical Analysis and Applications》2007,335(2):882-901
If F is a set-valued mapping from Rn into Rm with closed graph, then y∈Rm is a critical value of F if for some x with y∈F(x), F is not metrically regular at (x,y). We prove that the set of critical values of a set-valued mapping whose graph is a definable (tame) set in an o-minimal structure containing additions and multiplications is a set of dimension not greater than m−1 (respectively a σ-porous set). As a corollary of this result we get that the collection of asymptotically critical values of a set-valued mapping with a semialgebraic graph has dimension not greater than m−1. We also give an independent proof of the fact that a definable continuous real-valued function is constant on components of the set of its subdifferentiably critical points. 相似文献
15.
The growth theorem and the 1/2-covering theorem are obtained for the class of normalized biholomorphic convex mappings on
bounded convex circular domains, which extend the corresponding results of Sufridge, Thomas, Liu, Gong, Yu, and Wang. The
approach is new, which does not appeal to the automorphisms of the domains; and the domains discussed are rather general on
which convex mappings can be studied, since the domain may not have a convex mapping if it is not convex.
Project supported by the National Natural Science Foundation of China and the State Education Commission Doctoral Foundation. 相似文献
16.
Alexander J. Zaslavski 《Numerical Functional Analysis & Optimization》2013,34(1-2):215-240
In this work we study the asymptotic behavior of optimal trajectories for a class of superlinear mappings arising in economic dynamics. We establish the existence of an open everywhere dense subset F of the space of set-valued mappings such that each mapping fron F has the turnpike property. 相似文献
17.
Takamitsu Yamauchi 《Topology and its Applications》2012,159(4):1219-1222
We show selection theorems for set-valued mappings with finite-dimensional convex values, one of which is a partial extension of a selection theorem due to S. Barov (2008) [1]. 相似文献
18.
19.
20.
《Optimization》2012,61(11):2227-2245
ABSTRACTIn this paper, we present a new set-valued Lagrange multiplier theorem for constrained convex set-valued optimization problems. We introduce the novel concept of Lagrange process. This concept is a natural extension of the classical concept of Lagrange multiplier where the conventional notion of linear continuous operator is replaced by the concept of closed convex process, its set-valued analogue. The behaviour of this new Lagrange multiplier based on a process is shown to be particularly appropriate for some types of proper minimal points and, in general, when it has a bounded base. 相似文献