半严格不变凸函数

文章在Banach空间中定义了一种新的广义凸函数—半严格不变凸函数.对于满足局部Lipschitz条件的半严格不变凸函数,得到了它的广义Clarke次微分性质.文中还讨论了半严格不变凸函数与不变凸函数及半严格预不变凸函数之间的关系,得到了半严格不变凸函数的一些性质.     

半严格不变凸函数

文章在Banach空间中定义了一种新的广义凸函数—半严格不变凸函数.对于满足局部Lipschitz条件的半严格不变凸函数,得到了它的广义Clarke次微分性质.文中还讨论了半严格不变凸函数与不变凸函数及半严格预不变凸函数之间的关系,得到了半严格不变凸函数的一些性质.     

非自反Banach空间中的度量投影

该文给出非自反Banach空间中一类超平面上度量投影的表达式．在近严格凸Banach空间中,研究了它们的连续性．对于对偶Banach空间X*,给出弱*闭子集上度量投影的一些连续性结果．     

抽象度量空间上的一致连续函数空间

本文主要讨论抽象度量空间上的一致连续函数空间的Banach空间结构,代数结构和格结构．     

Banach空间中线性算子的(集值)度量广义逆的表示及应用

在Banach空间Y无自反和从Banach空间X到Y的线性算子T无闭值域和稠定的假定下,利用Banach空间几何方法证明了Banach空间中线性算子的度量广义逆是具有闭凸值的集值映射,建立了该度量广义逆的存在性、唯一性和等价表达式,并给出了此表达式的一个应用示例．所得的部分结果本质地拓广王玉文和潘少荣在Banach空间Y自反,从X到Y的线性算子T为闭值域和稠定的假定下的近期相应结果．     

Banach空间中线性算子的(集值)度量广义逆及其齐性单值选择

为研究Banach空间中不适定线性算子方程的最佳逼近解,Nashed在文[1]中引入了Banach空问中线性算子T的(集值)度量广义逆T的概念,并提出“求解线性算子的(集值)度量广义逆的具有良好性质的单值选择是值得研究”的公开问题.本文首先证明了Banach空间中线性算子的度量广义逆是具有闭凸值的集值映射,给出了该度量广义逆的等价表达式,并利用Banach空间的再赋范方法,给出其有界齐性的单值选择,部分地解决了Nashed所提出的公开问题.     

任意Banach空间中线性算子的Moore-Penrose度量广义逆

在无空间严格凸的几何假定下,利用Banach空间几何方法给出了任意Banach空间中线性算子T的Moore-Penrose度量广义逆T~+的存在性、唯一性、极小性和线性性的充要条件,同时还讨论了T~+的一些性质,这些本质地将文献[8]的最近结果从严格凸Banach空间拓广至任意Banach空间．     

Banach空间的p— Asplund 伴随空间

我们称一个定义在Banach空间E上的连续凸函数f具有Frechet可微性质（FDP）,如果E上的每个实值凸函数g≤f均在E一个稠密的Gδ－子集上Frechet可微。本文主要证明了：对任何Banach空间E,均存在一个局部凸相容拓扑p使得1）（E,p)是Hausdorff局部凸空间;2） E上的每个范数连续具有FDP的凸函数均是p－连续的;3）每个p-连续的凸函数均具有FDP ;4）p等价某个范数拓扑当且仅不E是Asplund空间。     

多值Bregman全拟渐近非扩张映像的强收敛性

建立了一种算法,用以寻求自反Banach空间中多值Bregman全拟渐近非扩张映像的有限族的公共不动点,改进和推广了以前的结果(算法是基于与一凸函数有关的Bregman距离).最后,把所得的结果应用于平衡系统问题,自反Banach空间中极大单调映像的零点问题.     

Banach空间闭超平面上度量投影的连续性

该文给出Banach空间X的对偶空间X~*中闭超平面上度量投影的表达式,并在Banach空间中研究了闭超平面上度量投影的连续性.     

On the Equivalence of the Mizoguchi-Takahashi Locally Contractive Map and the Nadler’s Locally Contractive Map

Abstract

In this paper, the equivalence between multi-valued maps satisfying the Mizoguchi-Takahashi’s uniformly locally contractive condition and multi-valued maps satisfying the Nadler’s uniformly locally contractive condition is obtained on metrically convex space. We have provided examples to illustrate that this equivalence need not be true on any arbitrary metric space.     

On a proximal point method for convex optimization in banach spaces

We analyze the behavior of a parallel proximal point method for solving convex optimization problems in reflexive Banach spaces. Similar algorithms were known to converge under the implicit assumption that the norm of the space is Hilbertian. We extend the area of applicability of the proximal point method to solving convex optimization problems in Banach spaces on which totally convex functions can be found. This includes the class of all smooth uniformly convex Banach spaces. Also, our convergence results leave more flexibility for the choice of the penalty function involved in the algorithm and, in this way, allow simplification of the computational procedure.     

Convex functions, subdifferentiability and renormings

This paper through discussing subdifferentiability and convexity of convex functions shows that a Banach space admits an equivalent uniformly [locally uniformly, strictly] convex norm if and only if there exists a continuous uniformly [locally uniformly, strictly] convex function on some nonempty open convex subset of the space and presents some characterizations of super-reflexive Banach spaces. Supported by NSFC     

Closed convex hulls,contents, and K‐spectral states

Our general result says that the closed convex hull of a set K consists of barycentres of probability contents (i.e., finitely additive set functions) on K. (Here K can be any nonempty subset of any nonempty compact convex set in any real or complex locally convex Hausdorff vector space.) In the equivalent setting of dual spaces, we give a very handy analytic criterion for a linear functional to be in the closed convex hull of a given nonempty point‐wise bounded set K of linear functionals (under some mild additional assumption). This is the notion of a K‐spectral state. Our criterion enhances the Abstract Bochner Theorem for unital commutative Banach *‐algebras (which easily follows from our result), in that it allows us to prescribe the set K on which a representing content should live. The content can be chosen to be a Radon measure if K is weak* compact. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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

本文把「３」的主要结果从Ｈｉｌｂｅｒｔ空间推广到一致凸的Ｂａｎａｃｈ空间,证明了一致凸的Ｂａｎａｃｈ空间上的渐近非扩张映象的迭代序列的收敛性。     

Conjugacy relationship between M-convex and L-convex functions in continuous variables

By extracting combinatorial structures in well-solved nonlinear combinatorial optimization problems, Murota (1996,1998) introduced the concepts of M-convexity and L-convexity to functions defined over the integer lattice. Recently, Murota–Shioura (2000, 2001) extended these concepts to polyhedral convex functions and quadratic functions in continuous variables. In this paper, we consider a further extension to more general convex functions defined over the real space, and provide a proof for the conjugacy relationship between general M-convex and L-convex functions.Mathematics Subject Classification (1991): 90C10, 90C25, 90C27, 90C35This work is supported by Grant-in-Aid of the Ministry of Education, Culture, Sports, Science and Technology of Japan     

DIFFERENTIABILITY OF CONVEX FUNCTIONS ON SUBLINEAR TOPOLOGICAL SPACES AND VARIATIONAL PRINCIPLES IN LOCALLY CONVEX SPACES

This paper presents a type of variational principles for real valued w lower semicon-tinuous functions on certain subsets in duals of locally convex spaces, and resolve a problem concerning differentiability of convex functions on general Banach spaces. They are done through discussing differentiability of convex functions on nonlinear topological spaces and convexification of nonconvex functions on topological linear spaces.     

Banach空间上Ptolemy常数的计算

利用绝对正规范数生成凸函数的关系,给出了加权平均范数空间上Ptolemy常数的取值,解决了一些文献的遗留问题,并在一些具体的空间上给出了Ptolemy常数的新结果.     

A REMARK ON DUALITY FOR THE SUM OF CONVEX FUNCTIONS IN GENERAL BANACH SPACES

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