集值映射的Nash平衡点集的通有稳定性

本文讨论了集值映射的Nash平衡点的存在及平衡点集的通有稳定性,得到大多数的集值映射的Nash平衡点集是稳定的。     

Banach空间中双扰动超有效性的稳定性(英)

在Ｂａｎａｃｈ空间中讨论了超有效点的稳定性．在半连续的意义下,给出了当约束集和控制锥同时扰动时,超有效点的稳定性．     

拟半连续格和交半连续格

作为半连续格的推广, 引入了拟半连续格的概念. 讨论了拟半连续格的基本性质. 在拟半连续格上得到了类似于拟连续偏序集的一些主要结果. 同时探讨了半连续格、拟半连续格、交半连续格、交连续格、强连续格几种不同结构之间的关系. 最后,讨论了半连续函数空间仍是半连续格的条件.     

半连续格上的拓扑

该文引入半连续格上的几个拓扑并讨论了它们的性质及它们之间的相互关系.     

Orlicz空间上支撑映射的半连续性

给出赋Luxemburg范数的Orlicz空间上支撑映射上（下）半连续的判别准则。     

两类单边算子的半连续性研究

本文研究了单边Hardy-Littlewood极小算子的上半连续性及单边Hardy-Littlewood极大算子的下半连续性问题.利用半连续性的相关性质和新型集合测度估计等获得了单边Hardy-Littlewood极小算子m~+f(x)在R~n上的上半连续性和单边Hardy-Littlewood极大算子M~+f(x)在R~n上的下半连续性,推广了Hardy-Littlewood极大算子的半连续性成果.     

二阶微分包含的边值问题及其应用

在Banach中讨论了一类二阶微分包含的边值问题和一类反馈控制问题.结合不动点定理,对解的存在性给出了两个充分性条件,最后应用前面的结果建立了反馈控制问题解的存在性定理.     

关于多值映象连续性的两个例子

本文在R²中构造了两个十分简单的多值映象的例子:第一个说明准上半连续(?)上半连续;第二个说明弱上半连续(?)准上半连续。     

伪度量函数的一个应用

本文用伪度量函数来讨论映射中的不动点定理,推广了文[1][2]中的一些结 果．     

半连续格的刻画和映射

本文讨论了半连续格的一些性质,在半连续格中引入半Scott开集族,用半Scott开集族来刻画半连续格,同时定义了半连续格之间的半连续映射,得到闭包算子的像仍是半连续格的条件.最后,研究了半连续格上的半连续映射的全体不动点之集的性质。     

广义凸空间上重合点定理和极大极小不等式

利用已知的KKM型定理,在广义空间上得到若干个新的重合点定理和推广的Fan-Browder型不动点定理,并且讨论了Von Newmann-Sion型极大极小不等式.主要结果改进和推广了文献中的相应结论.     

Relaxation and existence of optimal controls for systems governed by evolution inclusions in separable Banach spaces

In this paper, we examine relaxed control systems governed by evolution inclusions in a separable Banach space. First, we establish the existence of admissible trajectories, correcting an earlier result of Ahmed. Then, we obtain a compactness result for the set of admissible trajectories. Using this compactness result, we prove the existence of optimal solutions for optimal control problems; furthermore, we show that the values of the original and relaxed problems are equal. Finally, we show that the original trajectories are dense in the set of relaxed trajectories. An example is worked out.This research was supported by NSF Grant No. DMS-86-02313.     

一类集值投入产出方程的可解性结果

A class of set-valued Leontief input-output equation is introduced and two solvability theorems are obtmned,which provide some corresponding existence,surjection as well as continuity results.     

On Optimization Properties of Functions, with a Concave Minorant

We give a definition of the class of functions with a concave minorant and compare these functions with other classes of functions often used in global optimization, e.g. weakly convex functions, d.c. functions, Lipschitzian functions, continuous and lower semicontinuous functions. It is shown that the class of functions with a concave minorant is closed under operations mainly used in optimization and how a concave minorant can be constructed for a given function.     

LIPSCHITZ STABILITY OF GENERAL CONTROL SYSTEMS Ⅱ.IN TERMS OF TWO MEASURES

1IntroductionStabilityintermsoftwomeasures,thisconceptenableustounifyava-rietyofstabilityconceptsandtoofferageneralandunifiedframeworkforinvestigationofstabilitytheory.AndtheoriginalLiapunovtheoremshavebeenextended,generalizedandweakenedinvariousaspects[3…     

Fixed points and quasi-equilibrium problems

A fixed-point theorem for compact acyclic maps defined on convex subsets of notnecessarily locally convex topological vector spaces is applied to the existence of solutions of quasi-equilibrium problems. Such existence theorems extend known ones which were used for unified approaches to quasi-variational inequalities in [1–5] and others.     

von Neumann代数交叉积的注记

设A是B(H)中的极大交换*-子代数, G是离散群,在不要求G自由地作用在A的情况下,得到了交叉积A×αG是因子的充分且必要条件.     

A Method for Converting a Class of Univariate Functions into d.c. Functions

D.c. functions are functions that can be expressed as the sum of a concave function and a convex function (or as the difference of two convex functions). In this paper, we extend the class of univariate functions that can be represented as d.c. functions. This expanded class is very broad including a large number of nonlinear and/or nonsmooth univariate functions. In addition, the procedure specifies explicitly the functional and numerical forms of the concave and convex functions that comprise the d.c. representation of the univariate functions. The procedure is illustrated using two numerical examples. Extensions of the conversion procedure for discontinuous univariate functions is also discussed.     

Periodic solutions for a class of differential inclusions in general Banach spaces

Let X be a real Banach space, an m-accretive operator and a multi-function which is 2π-periodic with respect to its first argument, has nonempty, closed, convex and weakly compact values and is strongly-weakly upper semicontinuous. In this paper we prove the existence of at least one solution for the problem