关于一致凸的Banach空间上的渐近非扩张映象的迭代序列的收敛性定理的注记

本文研究了在一致凸Banach空间中定义在闭凸集C上渐近非扩张映象T不动点的迭代问题,我们的讨论去掉了在刘和薛[2]中C是有界的假设.     

Banach空间中渐近正则半群的不动点定理

设X是p一致凸Banach空间,具有弱一致正规结构与非严格的Opial性质.又设C是X的非空凸弱紧子集.在适当的条件下,证明了C上每个渐近正则半群T={T(t):t∈S}都有不动点进一步,在类似的条件下,也讨论了一致凸Banach空间中渐近正则半群的不动点的存在性.     

Banach空间中渐近正则半群的不动点定理

设X是p一致凸Banach空间,具有弱一致正规结构与非严格的Opial性质.又设C是X的非空凸弱紧子集.在适当的条件下,证明了C上每个渐近正则半群T={T(t)t∈S}都有不动点.进一步,在类似的条件下,也讨论了一致凸Banach空间中渐近正则半群的不动点的存在性.     

基于最优D.C.分解的单二次约束非凸二次规划精确算法

本文提出一种基于最优D.C.分解的单二次约束非凸二次规划精确算法.本文首先对非凸二次日标函数进行D.C.分解,然后对D.C.分解中凹的部分进行线性下逼近得到一个凸二次松弛问题.本文证明了最优D.C.分解可通过求解一个半定规划问题得到,而原问题的最优解可以通过计算最优凸二次松弛问题的满足某种互补条件的解得到.最后,本文报告了初步数值计算结果.     

一致凸Banach空间中非扩张映射的Ishikawa迭代

本文研究在一致凸Banach空间中,Ishikawa迭代的性质.在不假定C有界以及limsup\limitss     

凸体的两个几何量在Steiner对称化下的变化及其应用

本文研究了凸体的某些几何量在Steiner对称化作用下的变化情况.设C和D是d维欧氏空间R~d中的两个凸体,我们表明凸体关于特殊线性群SL(d)的极小表面积min{S(ΦC):Φ∈SL(d)}和混合体积V(C,D,…,D)分别在Steiner对称化作用后是不增加的.作为上述结果的应用,混合体积的Minkowski第一不等式被重新证明.     

完备向量格的凸集分离定理及其应用

本文指出凸集分离定理对完备向量格的下列推广结果。 设X为线性空间,Y为完备向量格,C为X×Y中的凸锥。如果C满足 1)G_Y={y∈Y|(0,y)∈C}有下界; 2)存在y∈Y,使得 V_X={x∈X|(x,y)∈C}为X中的吸收集,那末存在线性映射∧:X→Y,使得 ∧x+y≥0,?(x,y)∈C。 用这一结果可以完善地把凸规划的Kuhn-Tucker定理推广到凸向量规划情形,改进了Zowe的结果。     

关于多元多项式凸逼近

§1.引言 在多项式保形逼近理论中面临以下两个基本问题: 问题1.对于k≥2,R~k中是否存在k维紧凸集E及C(E)上的保凸正线性算子列L_n:C(E)→P_n满足:?凸函数f∈C(E),||L_nf-f||_E→0(n→∞)? 问题2.对于k≥2以及R~k中的任意k维紧凸集E和任意凸函数f∈C(E),是否存在一列多项式p_n∈P_n,使每一个p_n在E上为凸函数,并且||p_n-f||_E→0(n→∞)?     

（C—K）性质的特征

该文绘出（C－K），K=Ⅰ，Ⅱ，Ⅲ正性质的一些充要条件，从而我们得到：如果Banach空间X有（C一Ⅲ）（（C－Ⅱ）；（C－Ⅰ）性质，则对X的任意赋范集AU（X*），单位球面S（X）上的σ（X，A）拓朴与弱拓扑（范数拓扑）等价且X近非常凸（近强凸；强凸）.     

关于渐近非扩张映象不动点迭代的一点注记

设E是一致凸Banach空间,C是E的非空闭凸子集,T:C→C是具有不动点的渐近非扩张映象．该文证明了在某些适当的条件下,由下列修改了的Ishikawa迭代程序所定义的序列{xn}=xn 1=rpn,pn=(1-an)xn anTmn ryn un,yn=(1-bn)xn bnTkn xn vn, (n≥1)弱收敛到t的不动点．     

Über die Approximation von lokal konvexen Mengen

While convex sets in Euclidean space can easily be approximated by convex sets with C -boundary, the C -approximation of convex sets in Riemannian manifolds is a non-trivial problem. Here we prove that C-approximation is possible for a compact, locally convex set C in a Riemannian manifold if (i) C has strictly convex boundary or if (ii) the sectional curvature is positive or negative on C.The proofs are based on a detailed analysis of the distance function from C, on results from [1] and on the Greene-Wu approximation process for convex functions ([5], [6]). Finally, using similar methods, a partial tubular neighborhood with geodesic fibres is constructed for the boundary of a locally convex set. This construction is essential for some results in [2].     

Fixed Point Theorems of Krasnosel’skii Type In Locally Convex Spaces and Applications to Integral Equations

The paper presents some fixed point theorems for operators of the form U + C on a bounded closed convex subset of a locally convex space, where C is completely continuous and Uⁿ satisfies contraction type conditions. Applications to integral equations in a Banach space are presented.     

Minima locaux,fonctions marginales et hyperplans séparants dans l'optimisation discrète

The goal of this Note is to prove results in optimization of two integer variables which correspond to fundamental results in convex analysis of real variables, viz. that a local minimum of a convex function is global; that the marginal function of a convex function is convex; and that two disjoint convex sets can be separated by a hyperplane. To cite this article: C.O. Kiselman, C. R. Acad. Sci. Paris, Ser. I 346 (2008).     

ON THE EXISTENCE OF FIXED POINTS FOR LIPSCHITZIAN SEMIGROUPS IN BANACH SPACES

61. Introduction and PreliminariesLet C be a nonempty subset Of a Banal spare X. Then a mapping T: C -- C is saidto be a LiPSdrizian maPPing if, for ear integer n 2 1, there eallts a constant km > 0' such that Ilaal ~ chill S k.llx ~ all for all ale E C. A Lipschitzian mapping T is saidto be ~ k-LiPSdszian if km = k for all n 2 1, nonerpansive if km = 1 for alln 2 1, eleCtively. Moreover, a maPPing T: C - C is called asymptotically regularll'191if Asllgu 'z ~ chill = 0 for all 2 E…     

Duality for Convex Monoids

Every C*-algebra gives rise to an effect module and a convex space of states, which are connected via Kadison duality. We explore this duality in several examples, where the C*-algebra is equipped with the structure of a finite-dimensional Hopf algebra. When the Hopf algebra is the function algebra or group algebra of a finite group, the resulting state spaces form convex monoids. We will prove that both these convex monoids can be obtained from the other one by taking a coproduct of density matrices on the irreducible representations. We will also show that the same holds for a tensor product of a group and a function algebra.     

The Empty Hexagon Theorem

Let P be a finite set of points in general position in the plane. Let C(P) be the convex hull of P and let Cⁱ_P be the ith convex layer of P. A minimal convex set S of P is a convex subset of P such that every convex set of P ∩ C(S) different from S has cardinality strictly less than |S|. Our main theorem states that P contains an empty convex hexagon if C¹_P is minimal and C⁴_P is not empty. Combined with the Erdos-Szekeres theorem, this result implies that every set P with sufficiently many points contains an empty convex hexagon, giving an affirmative answer to a question posed by Erdos in 1977.     

关于一致凸Banach空间中渐近非扩张半群的几乎轨道的渐近行为

设Ｘ是具有Ｆｒｃｈｅｔ可微范数的一致凸Ｂａｎａｃｈ空间，Ｃ是Ｘ的有界闭凸子集，Ｓ＝｛Ｔ（ｔ）：ｔ≥０｝是Ｃ上渐近非扩张牛群．若ｕ（·）：［０，＋∞）→Ｃ是Ｓ的几乎轨道且关于ｔ∈［０，＋∞）一致连续，则｛ｕ（ｔ）｝几乎弱收敛到集合　　｛ｕ（ｒ）：ｒ≥ｔ｝∩Ｆ（ｓ）的唯一点。     

Upper bounds for the perimeter of plane convex bodies

We show that the maximum total perimeter of k plane convex bodies with disjoint interiors lying inside a given convex body C is equal to $\operatorname{per}\, (C)+2(k-1)\operatorname{diam}\, (C)$ , in the case when C is a square or an arbitrary triangle. A weaker bound is obtained for general plane convex bodies. As a consequence, we establish a bound on the perimeter of a polygon with at most k reflex angles lying inside a given plane convex body.     

On Extreme Convex Subsets of the Plane

Let Q be a convex compact set in R2 with a non-empty interior. We denoteby C the family of all non-empty closed convex subsets of Q. The aim of thepaper is to characterize the extreme elements of C.