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.

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.

On <i>M</i>-Asymmetric Semi-Open Sets and Semicontinuous Multifunctions in Bitopological Spaces

The purpose of this paper is to introduce the notions of m-asymmetric semiopen sets and M-asymmetric semicontinuous multifunctions defined between asymmetric sets satisfying certain minimal conditions in the framework of bitopological spaces. Some new characterizations of m-asymmetric semiopen sets and M-asymmetric semicontinuous multifunctions will be investigated and several fundamental properties will be obtained.

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.

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.

KY FAN TYPE BEST APPROXIMATION THEOREM FOR A CLASS OF FACTORIZABLE MULTIFUNCTIONS

An existence result on Ky Fan type best approximation is proved. For this pur- pose, a class of factorizable multifunctions and the other one being a demicontinuous, rela- tive almost quasi-convex, onto function on an approximately weakly compact, convex sub- set of Hausdorff locally convex topological vector space are used. As consequence, this result extends the best approximation results of Basha and Veeramani[8] and many others.

Some Properties of Two Kinds of Multifunctions

Let X and Y be metrizable topological linear spaces. In this paper, the following results are proved. (1) If X and Y are complete, g: X→Y is a point closed u. s. c.,and symmetric process with F(X)=Y,then either F(X) is meager in Y,or else F is an open muRifunction with F(X)=Y. (2) If X is complete, and F: X→Y is a process with a subclosed graph, then F is I s. c.. We also discuss topological multi-homomorphisms between topological linear spaces.

Existence of Solutions to Generalized Vector Quasi-variational-like Inequalities with Set-valued Mappings

In this paper, we introduce and study a class of generalized vector quasivariational-like inequality problems, which includes generalized nonlinear vector variational inequality problems, generalized vector variational inequality problems and generalized vector variational-like inequality problems as special cases. We use the maximal element theorem with an escaping sequence to prove the existence results of a solution for generalized vector quasi-variational-like inequalities without any monotonicity conditions in the setting of locally convex topological vector space.

Uniform attractors for non-autonomous Klein-Gordon-Schrdinger lattice systems

The existence of a compact uniform attractor for a family of processes corre- sponding to the dissipative non-autonomous Klein-Gordon-SchrSdinger lattice dynamical system is proved. An upper bound of the Kolmogorov entropy of the compact uniform attractor is obtained, and an upper semicontinuity of the compact uniform attractor is established.

Global Attractors for Nonclassical Diffusion Equations of Kirchhoff Type

In this article, the well-posedness and long-time behavior of a nonclassical diffusion equation of Kirchhoff type are considered. Using the method of Galerkin approximation, the existence and uniqueness of solutions are proved. At last, the existence of global attractors and its upper semicontinuous property are discussed.

STABILITY OF MAJORLY EFFICIENT POINTS AND SOLUTIONS IN MULTIOBJECTIVE PROGRAMMING

In this paper, we obtain some other properties of the majorly efficient points and solutions of the multiobjective optimization presellted in two previous papers of Hu. By decomposing the major cone, which is non-pointed, non-convex and non-closed into a finite union of disjoint strictly supported pointed convex cones, we discuss the continuous perturbations of the decision space. Several sufficient conditions for the continuity of the sets of majorly efficiellt points and solutions are given.

Existence and stability of solutions to inverse variational inequality problems

In this paper, two new existence and quasi-variational inequality problems are theorems of solutions to inverse variational proved using the Fan-Knaster-Kuratowski- Mazurkiewicz （KKM） theorem and the Kakutani-Fan-Glicksberg fixed point theorem. Upper semicontinuity and lower semicontinuity of the solution mapping and the approximate solution mapping to the parametric inverse variational inequality problem are also discussed under some suitable conditions. An application to a road pricing problem is given.

Generalized Convexity and Generalized Quasi-variational Inequality

The properties of generalized convexity are studied in this paper,as well as an existence Theorem of solutions for a type of generalized quasi-variational inequality is then abtained.

The Level Structures of the Kernel and Hull on Lattice—Valued Funcetions and Induced Spaces

It is studied systematically for the level strcture of the kernel and hull on continuous-lattice- calued function.In terms of these results,the level characterixations of induced space are odtained.

Generalized Quasi-equilibrium Problems without Open Fibers

In this paper, we first prove some new selection and fixed point theorems in generalized convex spaces. Then, we establish some existence theorems of quasi-equilibrium and generalized quasi-equilibrium without the conditions of open fibers, by applying our selection and fixed point theorems.

ANOTHER FORM OF KKM TYPE THEOREM AND ITS APPLICATIONS ON GENERALIZED CONVEX SPACES

In this paper, another form of KKM type theorem on generalized convex spaces is obtained and the problems of von Neumann-Fan type sup inf sup inequalities and variational inequalities are discussed for their applications.The main results improve and generalize the corresponding results in previous papers.

On the Weak Drop Property for Polar of Closed Bounded Convex Sets

We define and study the weak drop property for the polar of a closed bounded convex set in a Banach space which is both a generalization of the weak drop property for dual norm in a Banach space and a characterization of the sub-differential mapping x →(?)p(x) from S(X) into 2S(X) that is norm upper semi-continuous and norm compact-valued.

Continuity of the Solution Mappings for Parametric Generalized Strong Vector Equilibrium Problems

The stability analysis of the solution mappings for vector equilibrium problems is an important topic in optimization theory and its applications. In this paper, we focus on the continuity of the solution mapping for a parametric generalized strong vector equilibrium problem. By virtue of a nonlinear scalarization technique, a new density result of the solution mapping is obtained. Based on the density result, we give sufficient conditions for the lower semicontinuity and the Hausdorff upper semicontinuity of the solution mapping to the parametric generalized strong vector equilibrium problem. In addition, some examples were given to illustrate that our results improve ones in the literature.

Some Theorems for Real Increasing Functions in Elementary Fixed Point Theory

We obtain some theorems for real increasing functions showing that elementary fixed point theory can bring to astonishing results by assuming only a few properties, some of which intrinsically possessed from these functions. An application is given for a theorem of quasi-compactness and a known result in posets is also recalled and applied to real intervals.