Upper and Lower Semicontinuity of Solution Sets for Parametric Generalized Vector Quasi-equilibrium Problems

In this paper, two kinds of parametric generalized vector quasi-equilibrium problems are introduced and the relations between them are studied. The upper and lower semicontinuity of their solution sets to parameters are investigated.

LOWER SEMICONTINUITY OF A CLASS OF FUNCTIONALSIN SBV_H

In this paper lower semicontinuity of the functional I(u)=∫_Ωf(x,u,Δ~ _Hu)dx is investigated for f being a Carathéodory function defined on Hn×R×R^2n and for u∈SBV_H(Ω),where Hn is the Heisenberg group with dimension 2n+1,ΩHn is an open set and Δ~ _Hu denotes the approximate derivative of the absolute continuous part Da_Hu with respect to D_Hu.In addition,a Lusin type approximation theorem for a SBV_H function is proved.

Lower Semicontinuity of the Effcient Solution Mapping in Semi-In?nite Vector Optimization

This paper establishes some suffcient conditions for the lower semicontinuity of the effcient solution mapping for the semi-infinite vector optimization problem with perturbations of both the objective function and the constraint set in normed linear spaces. The constraint set is the set of weakly effcient solutions of vector equilibrium problem, and perturbed by the perturbation of the criterion mapping to the vector equilibrium problem.

A Lower Semicontinuity Result for Some Integral Functionals in the Space SBD

In this paper, we obtain a lower semicontinuity result with respect to the strong L1-convergence of the integral functionals F（u,Ω）=Ωf（x,u（x）,εu（x））dx defined in the space SBD of special functions with bounded deformation. Here Su represents the absolutely continuous part of the symmetrized distributional derivative Eu. The integrand f satisfies the standard growth assumptions of order p 〉 1 and some other conditions. Finally, by using this result,we discuss the existence of an constrained variational problem.

Lower Semicontinuity of the Solution Sets to Parametric Generalized Vector Equilibrium Problems

In this paper,by a scalarization method,the lower semicontinuity of the solution mappings to two kinds of parametric generalized vector equilibrium problems involving set-valued mappings is established under new assumptions which are weaker than the C-strict monotonicity.These results extend the corresponding ones.Some examples are given to illustrate our results.

UPPER SEMICONTINUITY OF ATTRACTORS FORTHE REACTION DIFFUSION EQUATION

This paper deals with the reaction diffusion equation in domain, Omega = R or Omega = (-L, L) with L < infinity. Let A(L) and A be the global attractor of this equation corresponding to Omega = (-L,L) and Omega = R, respectively. It is showed that the global attractor A is upper semicontinuity at 0 with respect to the sets {A(L)} in some sense.

Almost Fixed Points and Fixed Points of Upper [Lower] Semicontinuous Multimap on Locally G-convex Spaces

In this paper, we use the well known KKM type theorem for generalized convex spaces due to Park （Elements of the KKM theory for generalized convex spaces, Korean J. Comp. Appl. Math., 7（2000）, 1-28） to obtain an almost fixed point theorem for upper [resp., lower] semicontinuous multimaps in locally G-convex spaces, and then give a fixed point theorem for upper semicontinuous multimap with closed Γ-convex values.

UPPER SEMI-CONTINUITY OF RANDOM ATTRACTORS FOR A NON- AUTONOMOUS DYNAMICAL SYSTEM WITH A WEAK CONVERGENCE CONDITION

In this paper,we develop the criterion on the upper semi-continuity of random attractors by a weak-to-weak limit replacing the usual norm-to-norm limit.As an application,we obtain the convergence of random attractors for non-autonomous stochastic reactiondiffusion equations on unbounded domains,when the density of stochastic noises approaches zero.The weak convergence of solutions is proved by means of Alaoglu weak compactness theorem.A differentiability condition on nonlinearity is omitted,which implies that the existence conditions for random attractors are sufficient to ensure their upper semi-continuity.These results greatly strengthen the upper semi-continuity notion that has been developed in the literature.

Inverse Limit of Spaces of Upper Semicontinuous Functions

Given a compact Hausdorff space X, U(X) denotes the compact Hausdorff space of all the upper semicontinuous functions from X to the unit interval with the dual lim inf topology. Then U is an endofunctor on compact Hausdorff space. It is proved in this note that this functor preserves inverse limits.

Upper Semicontinuity and Kolmogorov ε-Entropy of Global Attractor for κ-Dimensional Lattice Dynamical System Corresponding to Klein-Gordon-SchrSdinger Equation

In this paper, we establish the existence of a global attractor for a coupled κ-dimensional lattice dynamical system governed by a discrete version of the Klein-Gordon-SchrSdinger Equation. An estimate of the upper bound of the Kohnogorov ε-entropy of the global attractor is made by a method of element decomposition and the covering property of a polyhedron by balls of radii ε in a finite dimensional space. Finally, a scheme to approximate the global attractor by the global attractors of finite-dimensional ordinary differential systems is presented .

Upper Semicontinuity of Parametric Lexicographic Vector Equilibrium Problems

In this paper, lexicographic vector equilibrium problems are investigated. By using the idea of sequential process, the upper semicontinuity and closedness of the solution set map are established for a parametric lexicographic strong vector equilibrium problem.

α-预不变凸函数的若干性质

考虑了一类广义凸函数——α-预不变凸函数,利用中间点的α-预不变凸性,讨论了α-预不变凸函数与半连续函数之间的关系,得到了α-预不变凸函数的一些性质.

预不变凸模糊数值函数及其应用

利用本文所定义的上(下)半连续,在一种新序意义下讨论了预不变凸模糊数值函数的若干判定定理.特别地,给出了预不变凸模糊数值函数的刻划定理.最后,作为应用,讨论了一类模糊数学规划问题的严格局部最优解和全局最优解存在的条件.

反凸模糊集

给出了反凸模糊集的定义并在此定义下推得了反凸模糊集的一些重要的性质,得到了模糊集是反凸模糊集的一些充分条件.

FC-度量空间中的一般拟平衡问题及其对约束多目标对策的应用

利用KKM技巧,建立了非紧完备FC-度量空间中关于一般拟平衡问题的平衡存在性定理.作为应用,获得了该空间中的约束多目标对策的加权Nash平衡存在性定理.

局部凸拓扑矢量空间内的广义拟变分不等式(英文)

设X是局部凸空间E的仿紧凸子集 ,F :X→ 2 X 是集值映象 ,φ :X×X→R是实泛函 .研究下列抽象广义拟变分不等式 (AGQVI) :求 ^x∈X使得 ^x∈F(^x)和 φ(^x ,y)≤ 0 , y∈F(^x) ,其中 φ(x ,y)关于x是 0 转移紧下半连续的和关于y是 0 对角拟凹的 .作为应用 ,作者得到了最近文献中关于广义拟变分不等式的很多已知结果的推广 .

非连续的广义拟变分不等式问题的存在性定理

考虑了广义拟变分不等式问题给一个实的赋范空间E,它的共轭空间是E,给定两个多值函数GX→2X,FX→2E,要找到(x-,φ-)∈X×E,使得x-∈G(x-),φ-∈F(x-),〈φ-,x--y〉≤0,y∈G(x-).把近来在E为有限维空间的假设下得到的一些存在性结果推广到无穷维空间中去,并对没有假设多值函数F任何的连续性的情形进行了研究.

抽象经济均衡问题解的存在性及其算法

本文首先研究一类新的向量均衡问题,利用截口定理与KKM定理两种不同的工具证明此类均衡问题解的存在性,接着,把这类向量均衡问题推广到更为一般的情形,随后讨论了具有上下界的均衡问题,它是由Isac,Sehgal和Singh于1999年提出的一个公开问题,本文在一定条件下获得了一个新的解的存在性定理,并构造了一个迭代算法,讨论了算法的收敛性。

无约束非光滑优化的信赖域算法

提出了一个处理无约束非光滑优化问题的信赖域算法 .它仅要求目标函数是下半连续的 ,而不是光滑的 ,或凸的 ,或局部Lipschitzian的 ,从而扩大了信赖域方法的使用范围 .

用近似凸性研究拟凸函数

用集合的近似凸性研究函数的拟凸性.在较弱假设下,获得了拟凸性的一些等价条件.