一类不可微规划的高阶对称对偶性

本文我们利用一个可微函数给出了一对高阶对称规划问题 ,其中目标函数包含了Rn 中一紧凸集的支撑函数 .在引入高阶F 凸性 (F 伪凸性 ,F 拟凸性 )后 ,证明了高阶弱、高阶强及高阶逆对称对偶性质 .     

在抽象凸结构中的逼近选择定理及其应用

本文首先建立了一个新的逼近选择定理,然后作为这个定理的应用,给出对于非H-凸像集值映射的一个不动点定理.     

在抽象凸结构中的逼近选择定理及其应用

本文首先建立了一个新的逼近选择定理,然后作为这个定理的应用,给出对于非H-凸像集值映射的一个不动点定理.     

图像面积有限的集值映射

该文利用集值映射得到了一个对有界变差函数的刻画.由此证明了对任意的有闭,凸像的上半连续集值映射F,如果其图像面积有限,则存在一有界变差函数f是F的可数选择.而且F的rectifiable图像可被光滑函数图像以流意义弱逼近和图像面积强逼近.     

代数上非原子集值测度的凸性

Z.Artstein证明了:σ—代数上的非原子有界集值测度是凸的,本文用简捷的方法得到: 定理设F为论域Ω上的代数,π为F上的非原子紧集值测度,则π为凸的,即A∈F,π(A)为凸集。 首先我们给出     

F分布的几个性质

F分布的概率密度函数中出现了Gamma函数和两个不同的参数.借助微积分的相关理论,固定F分布的密度函数中的一个参数,当另一个参数取不同值时,给出相应曲线的交点范围,同时研究F分布的密度函数的凸性.     

广义次似凸集值优化的对偶定理

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.     

Hilbert空间中的非扩张映象的不动点集的结构及其迭代集合序列逼近

我们研究Hilbert空间H中的闭凸集C上的非扩张映象T的不动点集F(T)的结构和它的集合序列逼近。我们得到 1 不动点集F(T)是闭的和凸的; 2 提供一个集合序列迭代法,使得由这个方法构造的迭代集合序列在某些条件和某种意义下强(弱)收敛于T的一个不动点,并给出收敛速度估计。 前面叙述的这些结果包含了Browder,Petryshyn,Kirk等人的某些结果。     

凸模糊子集的再定义

给出基于t-范上的凸模糊子集的定义,讨论这种凸模糊子集的同态像性质,重点研究了Tm-凸模糊子集的生成线,证明每一个TA－凸模糊子集为凸子集生成的Tm-凸模糊子集。     

平均凸曲线缩短流的非坍塌性

本文主要研究了平面凸曲线缩短流的非坍塌性质.首先,我们给出了平面凸曲线非坍塌性的定义,并通过定义一个函数Z,我们证明了平面凸曲线非坍塌与函数Z的非负性是等价的.接着,我们利用极值原理证明平面凸曲线缩短流保持非坍塌性质.     

对Aubin与Frankowska关于闭凸集值映射最小选择的一个结果的讨论

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     

Non-convex perturbations of maximal monotone differential inclusions

We give an existence result for \(\dot x \in -- Ax + F(x)\) whereA is a maximal monotone map andF is a set-valued map, with images not necessarily convex.     

Some remarks on a theorem on sets with connected sections

In this paper we give a complete answer to a question which naturally arises in comparing classical results of F. E. Browder and K. Fan on sets with convex sections with a recent result of B. Ricceri on sets with connected sections.     

Finding Convex Sets in Convex Position

Let F{\cal{F}} denote a family of pairwise disjoint convex sets in the plane. F{\cal{F}} is said to be in convex position, if none of its members is contained in the convex hull of the union of the others. For any fixed k 3 5k\ge5, we give a linear upper bound on P_k(n)P_k(n), the maximum size of a family F{\cal{F}} with the property that any k members of F{\cal{F}} are in convex position, but no n are.     

On quasi-umbilical locally strongly convex homogeneous affine hypersurfaces

In this paper, by developing the techniques of F. Dillen and L. Vrancken in [6], we study quasi-umbilical locally strongly convex homogeneous unimodular-affine hypersurfaces. We will present a characterization of a certain subclass in all dimensions; finally, in dimension five, we will give a complete classification of all quasi-umbilical homogeneous unimodular-affine hypersurfaces.     

Approximation to a set-valued mapping,I: A proposal

Given a multivalued mappingF, we address the problem of finding another multivalued mappingS that agrees locally withF. We limit ourselves to the case whenF(x) is convex compact for eachx. We propose anS obtained by linearizing the support function ofF(x) and give conditions under which thisS approximatesF in the sense of Hausdorff distance. We show equality betweenS and other proposals obtained from tangent cones to the graph ofF. Finally, we apply these results to the approximate subdifferential of a convex function.     

The Katchalski-Lewis Transversal Problem in R<Superscript>n</Superscript>

Let F be a family of disjoint translates of a compact convex set in the plane. In 1980 Katchalski and Lewis showed that there exists a constant k, independent of F, such that if each three members of F are met by a line, then a "large" subfamily G ⊂ F, with |F\G| ≤ k, is met by a line. In this paper we obtain a higher-dimensional analogue containing the Katchalski-Lewis result. Also we give two constructions of families of pairwise disjoint translates of the unit ball in R³ which answer some related questions.     

Inequalities in completely convex stochastic programming

A two-stage stochastic programming problem in which the random variable enters in a convex manner is called completely convex. For such problems we give a sequence of inequalities and equalities showing the equivalence of optimality over plans and optimality of a two-stage procedure related to dynamic programming and giving upper bounds on the expected value of perfect information. Our assumptions are the weakest possible to guarantee the results in the completely convex case and supersede previous related results which have received erroneous proofs or have been established under highly restrictive conditions. In the course of our argument we exhibit a new measurable selection theorem and a rather general form of Jensen's inequality. We also present a multistage generalization of our central theorem.     

Centroids, Centers, Medians: What is the Difference?

Consider a finite subset F of a real normed space. In this paper we try to evaluate the largest possible distance between pairs of points which are, for F, the centroid, a center, or a median. The results seem to show that only when X is a two-dimensional, strictly convex space, or when X is a Hilbert space, what the geometrical intuition indicates is more or less true. We give some examples showing some of the 'pathological' situations which can arise. Also, we indicate some open problems.