关于序列中紧空间的一些研究

主要是利用良序单调覆盖、内部保持覆盖刻画了序列中紧性.     

Banach空间的弱*序列紧性

本文研究了Ｂａｎａｃｈ空间的弱序列紧性．Ｂａｎａｃｈ空间Ｘ称为有（ｗ）性质，如果Ｘ（Ｘ的共轭空间）的每个有界序列有弱收敛子列．我们证明了，如果Ｂａｎａｃｈ空间Ｘ有（ｗ）性质，那么ｌｐ（Ｘ）（１≤ｐ＜＋∞）与ｃ０（Ｘ）也有（ｗ）性质．     

(L,M)-模糊拓扑空间中模糊紧性的测度

本文借助不等式,在(L,M)-拓扑空间中引入了模糊紧性度的概念,并讨论了它的性质.     

L-拓扑空间中一类新的SR-紧性

利用强半开L-集和它们的不等式在L-拓扑空间引入了一种新的SR-紧性,这里L是完备的DeMorgan代数。这种新的SR-紧性不依赖于格L的具体结构。当L是完全分配的DeMorgan代数时,给出了它的许多刻画。     

赋Orlicz范数的Musielak-Orlicz序列空间的单调点

给出赋Ｏｒｌｉｃｚ范数的Ｍｕｓｉｅｌａｋ－Ｏｒｌｉｃｚ序列空间中上（下）单调点以及上（下）局部一致单调点的充分必要条件．     

实序线性空间中用广义二阶锥方向导数刻画集值优化ε-全局真有效解

在实序线性空间中,利用ε-全局真有效点的性质,借助广义二阶锥方向邻接(相依)导数的定义,建立了不受约束集值优化问题ε-全局真有效元的二阶必要最优性条件,同时得到了受约束集值优化问题在ε-全局真有效解意义下的二阶充分最优性条件.     

直觉I-fuzzy拓扑空间中的(r,s)直觉模糊紧

介绍了直觉I-fuzzy拓扑空间中(r,s)直觉模糊半正规的定义,研究了直觉I-fuzzy拓扑空间中直觉弱连续、直觉弱开和直觉弱闭映射的等价定理及(r,s)直觉模糊紧,(r,s)直觉模糊殆紧、(r,s)直觉模糊几乎紧的相关定理.     

(h,φ )-Lipschitz函数及其广义方向导数和广义梯度

借助于Ben-Tal广义代数运算引进了一种新的函数--- (h,φ)-Lipschitz函数. 讨论了它与Lipschitz函数之间的关系,给出了它的广义方向导数和广义梯度,得到了它们的若干性质. 作为应用,给出了广义方向导数与切锥之间的关系.     

关于Banach空间中增生和伪压缩型映象迭代序列的收敛性问题

得出了Banach空间中增生和伪压缩型映象Ishikawa、Mann和最速下降序列强收敛于其不动点的充分必要条件.所得结果推广、改进和包含了某些最新的结果.     

Banach空间中Ishikawa迭代序列的稳定性和收敛性问题

在Banach空间的框架下,讨论了中间意义下的渐进非扩张的渐进伪压缩的具平均误差的修正的Ishikawa和Mann迭代序列的收敛性和稳定性之间的等价性问题,改进和推广了以前的结果.     

Generalized sequential normal compactness in Asplund spaces

Sequential normal compactness conditions are important properties in infinite-dimensional variational analysis and its applications. Following the recent study of the generalized sequential normal compactness (GSNC), this paper This paper reveals further applications of GSNC to the generalized differentiation theory in Asplund spaces, as well as the calculus of GSNC itself.     

局部β-凸空间的共轭锥与Hahn-Banach定理

由 [1 ],局部β-凸空间 X的共轭锥 X*β 取代共轭空间在局部β-凸分析中扮演核心角色 .本文第一部分在局部β-凸空间上给出β-次半范的 Hahn-Banach定理 ,第二部分通过共轭锥 ( X*β ,‖‖ )得到赋β-范空间 ( X,‖‖β)的可分性定理 ,第三部分给出局部 β-凸空间的共轭锥 X*β 在一致收敛拓扑下的完备性定理等 .     

局部β-凸空间中的第二分离性定理及其共轭锥上的有界性定理

第一部分给出局部β－凸空间中的第二分离性定理和Ｍｉｎｋｏｗｓｋｉ定理及Ｋｒｅｉｎ－Ｍｉｌｍａｎ定理等；第二部分得到其共轭锥上Ｕ Ｆ－有界与Ｕ Ｂ－有界等价的充要条件为原空间是次完备的．     

Proper minimal points of nonconvex sets in Banach spaces in terms of the limiting normal cone

In this paper, proper minimal elements of a given nonconvex set in a real ordered Banach space are defined utilizing the limiting (Mordukhovich) normal cone. The newly defined points are called limiting proper minimal (LPM) points. It is proved that each LPM is a proper minimal in the sense of Borwein under some assumptions. The converse holds in Asplund spaces. The relation of LPM points with Benson, Henig, super and proximal proper minimal points are established. Under appropriate assumptions, it is proved that the set of robust elements is a subset of the set of LPM points, and the set of LPM points is dense in that of minimal points. Another part of the paper is devoted to scalarization-based and distance function-based characterizations of the LPM points. The paper is closed by some results about LPM solutions of a set-valued optimization problem via variational analysis tools. Clarifying examples are given in addition to the theoretical results.     

On the Multiplicity and the Cohen-Macaulayness of Fiber Cones of Graded Modules

Let (A,m) be a Noetherian local ring with maximal ideal m,I an ideal of A,J an m-primary ideal of A,N a finitely generated A-module,S =⊕n≥0 Sn a finitely generated standard graded algebra over A and M =⊕n≥0 Mn a finitely generated graded S-module.We characterize the multiplicity and the Cohen-Macaulayness of the fiber cone FJ(M) =⊕n≥0 Mn/JMn.As an application,we obtain some results on the multiplicity and the Cohen-Macaulayness of the fiber cone ⊕n≥0 InN/JInN.     

锥方向导数和锥次梯度的性质及其在最优化中的应用

本文讨论了Ｗａｒｄ等人定义的锥方向导数和锥次梯度的性质，建立了一般数学规划的最优性Ｋｕｈｎ－Ｔｕｃｋｅｒ必要条件．     

Tangent Sets of Order One and Two to the Positive Cones of Some Functional Spaces

We compute the tangent cone and the tangent set of order two to the positive cone of some important functional spaces such as the space C(K) of continuous functions on a compact space and the space L_p(Q) of p-integrable functions on a measured space. The results are applied to the calculus of derivatives of order one and two of marginal functions. Accepted 19 April 1996     

齐型空间中的核条件下的T(1)定理

证明了齐型空间中的弱核条件下的T（1）定理。     

赋Orlicz范数下Orlicz-Lorentz序列空间的一致正规结构和一致非方性

Orlicz-Lorent空间作为经典Orlicz空间的推广,为调和分析及微分方程提供了合理的空间框架,而一致正规结构和一致非方性在不动点理论领域有着重要的应用.本文给出了赋Orlicz范数下Orlicz-Lorentz序列空间具有一致正规结构和一致非方性的充要条件.