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。     

Some new results on stability of Ekeland's ?-variational principle

In this paper, we give an example and point out that ?-solutions of Ekeland's variational principle are not always lower semicontinuous in infinite-dimensional Banach spaces, even with respect to the uniform metric. Further, the example shows that the ?-solutions need not be almost lower semicontinuous when the convergence of sequence of functions is weakened to Painlevé-Kuratowski epigraphical convergence. To provide some results of stability, we prove the almost lower semicontinuity of ?-solutions in a general framework.     

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。     

关于半连续函数与凸函数的注记

在半连续前提下,给出凸函数和严格凸函数的不等式刻划．指出非空凸集上的半连续函数满足中间点凸性时,成为凸函数,满足中间点严格凸性时,成为严格凸函数．最后定义F—G广义凸函数和条件p1,p2等概念,列举若干满足条件p1,p2的数量函数和向量函数,并指出,对于F—G广义凸函数,在条件p1,p2及一定连续性条件下,可以得到类似结果．     

集值映射的Nash平衡点的存在定理

本文引入了集值映射的Nash平衡点的概念，它以通常的Nash平衡点及Loose Nash平衡点为特例，并在紧和非紧的假设下，得到集值映射的Nash平衡点的存在定理，其中在非紧的情况下使用escaping序列的定义．     

凸函数与半连续函数的关系

通过研究凸函数与半连续函数的关系,给出了凸函数的一个与上半连续性相结合的等价定义.     

Topological degree of a family of convex functions and localization of nash equilibrium points

We define the degree of a family of convex functionsf _x, wherex , and prove that, if this degree is different from zero, one has at least one Nash equilibrium point in . This is a criterion of localization of such equilibrium points.     

Generalized Quasi-Variational Inequalities Without Continuities

Given a nonempty set and two multifunctions , we consider the following generalized quasi-variational inequality problem associated with X, : Find such that . We prove several existence results in which the multifunction is not supposed to have any continuity property. Among others, we extend the results obtained in Ref. 1 for the case (x(X.     

锥拟凸集值映射与集值映射的锥半连续性

本文借助锥界集定义了一种新的锥拟凸集值映射,并且利用广义Minkowski泛函讨论了锥半连续及锥外上半连续集值映射的锥拟凸性．     

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.     

A minimax theorem for functions with possibly nonconnected intersections of sublevel sets

We apply the selection theorem for multivalued mappings with paraconvex values (rather than various versions of KKM-principle) to prove several minimax theorems. In contrast with well-known minimax theorems for coordinatewise semicontinuous functions, in our theorems finite intersections of sublevel or uplevel sets can be nonempty and nonconnected.     

On Factorization Components of the Sojourn Times for Semicontinuous Random Walks in a Strip

We find an explicit form of the factorization components of the sojourn time for an upper semicontinuous random walk in a strip.     

一般拓扑空间上的KKM定理,匹配定理,重合点定理

引进没有任何凸结构的拓扑空间上的广义R-KKM映射的定义,并利用古典的KKM原理得到一般拓扑空间上的KKM型定理,然后利用该结果得到Lassonde型匹配定理和Klee型相交定理,最后作为应用给出非紧的拓扑空间上不动点定理和重合点存在定理.推广和改进了文献中的相应结果.     

On Fixed Point and Almost Fixed Point Problems of Lower Semicontinuous Type Multivalued Mappings

In the present paper, some new almost fixed point theorems and fixed point theorems for lower semicontinuous type multivalued mappings are obtained in metrizable H-spaces.     

一个极小极大定理

本文给出一个非线性结构的极小极大定理.设X是一个紧(Hausdorff)空间,是(X)的一个子集.如果对某个s∈(0,1),X关于是s-相似凹且对所有t∈(1/2,1),关于X是t-凸的.则inf sup_xf(x)=sup_xinf f(x). 我们的结果是Fan Ky,Konig H,Geraghty M A and Lin Bor-Luh相应结果的推广.     

函数的逼近及其在下半连续函数可微性中的应用

通过函数的下卷积函数列的逼近方法,在变分原理中从扰动最小值点集的“大小”入手,研究了下半连续函数的可微性。     

Monotone insertion of lattice-valued functions

Insertion of lattice-valued functions in a monotone manner is investigated. For L a ⊲-separable completely distributive lattice (i.e. L admits a countable base which is free of supercompact elements), a monotone version of the Katětov-Tong insertion theorem for L-valued functions is established. We also provide a monotone lattice-valued version of Urysohn’s lemma. Both results yield new characterizations of monotonically normal spaces. Moreover, extension of lattice-valued functions under additional assumptions is shown to characterize also monotone normality. This research was supported by the MEyC and FEDER under grant MTM2006-14925-C02-02/ and by UPV05/101     

变分泛函的半连续性问题

研究了非多项式增长的变分泛函,利用Orlicz空间理论,得到了其在Orlicz-Sobolev空间中弱序列下半连续的充要条件,推广了关于多项式增长的变分泛函的相应结论。