SYSTEM OF GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMS ON PRODUCT FC-SPACES

By applying a maximal element theorem on product FC-space due to author, some new equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in FC-spaces. By using these equilibrium existence theorems, some new existence theorems of solutions for the system of generalized vector quasi-equilibrium problems are established in noncompact product FC-spaces. These results improve and generalize some recent results in literature to product FC-spaces without any convexity structure.

NONEMPTY INTERSECTION THEOREMS AND SYSTEM OF GENERALIZED VECTOR EQUILIBRIUM PROBLEMS IN PRODUCT G-CONVEX SPACES

By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.

Systems of generalized vector quasi-variational inclusions and systems of generalized vector quasi-optimization problems in locally FC-uniform spaces

In this paper, we introduce some new systems of generalized vector quasi-variational inclusion problems and system of generalized vector ideal （resp., proper, Pareto, weak） quasi-optimization problems in locally FC-uniform spaces without convexity structure. By using the KKM type theorem and Himmelberg type fixed point theorem proposed by the author, some new existence theorems of solutions for the systems of generalized vector quasi-variational inclusion problems are proved. As to its applications, we obtain some existence results of solutions for systems of generalized vector quasi-optimization problems.

NONEMPTY INTERSECTION THEOREMS AND SYSTEM OF GENERALIZED VECTOR EQUILIBRIUM PROBLEMS IN PRODUCT G-CONVEX SPACES

By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.

GENERIC STABILITY AND EXISTENCE OF ESSENTIAL COMPONENTS OF THE SOLUTION SET FOR THE SYSTEM OF GENERALIZED VECTOR EQUILIBRIUM PROBLEMS

By using Fort theorem the generic stability result for the system of generalized vector equilibrium problems is established. Further, by proving the existence and connectivity of minimal essential set the existence result of essential components in the solution set is derived.

GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMSIN LOCALLY G-CONVEX SPACES

Some classes of generalized vector quasi-equilibrium problems ( in short, GVQEP) are introduced and studied in locally G-convex spaces which includes most of generalized vector equilibrium problems; generalized vector variational inequality problems, quasi-equilibrium problems and quasi-variational inequality problems as special cases. First, an equilibrium existence theorem for one person games is proved in locally G-convex spaces.. As applications, some new existence theorems of solutions for the GVQEP are established in noncompact locally G-convex spaces. These results and argument methods are new and completely different from that in recent literature.

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.

MATHEMATICAL PROGRAMS WITH SYSTEM OF GENERALIZED VECTOR QUASI-EQUILIBRIUM CONSTRAINTS IN FC-SPACES

In this article, four new classes of systems of generalized vector quasi-equilibrium problems are introduced and studied in FC-spaces without convexity structure. The notions of Ci（x）-FC-partially diagonally quasiconvex, Ci（x）-FC-quasiconvex, and Ci（x）-FC- quasiconvex-like for set-valued mappings are also introduced in FC-spaces. By applying these notions and a maximal element theorem, the nonemptyness and compactness of solution sets for four classes of systems of generalized vector quasi-equilibrium problems are proved in noncompact FC-spaces. As applications, some new existence theorems of solutions for mathematical programs with system of generalized vector quasi-equilibrium constraints are obtained in FC-spaces. These results improve and generalize some recent known results in literature.

System of Generalized Vector Quasi-Equilibrium Problems in Locally FC-Spaces

A new class of locally finite continuous topological spaces （for short, locally FC-spaces） and a class of system of generalized vector quasi-equilibrium problems are introduced. By applying a generalized Himmelberg type fixed point theorem for a set-valued mapping with KKM-property due to the author, a collectively fixed point and an equilibrium existence theorem of generalized game are first proved in locally FC-spaces. By applying our equilibrium existence theorem of generalized game, some new existence theorems of equilibrium points for the system of generalized vector quasi-equilibrium problems are proved in locally FC-spaces. These theorems improve, unify and generalize many known results in the literatures.

Solution to the Generalized Champagne Problem on simultaneous stabilization of linear systems

The well-known Generalized Champagne Problem on simultaneous stabilization of linear systems is solved by using complex analysis and Blonders technique. We give a complete answer to the open problem proposed by Patel et al., which automatically includes the solution to the original Champagne Problem. Based on the recent development in automated inequality-type theorem proving, a new stabilizing controller design method is established. Our numerical examples significantly improve the relevant results in the literature.

System of Generalized Symmetric Vector Quasi-Equilibrium Problems for Set-Valued Mappings

In this paper, a system of generalized symmetric vector quasi-equilibrium problems for set-valued mappings is introduced. By using a scalarization method and a fixed-point theorem, the existence result for its solution is established. The main result extends the corresponding results in Fu (J. Math. Anal. Appl. 285, 708–713, 2003) and Zhang, Chen and Li (OR Transactions 10, 24–32, 2006).

Existence of Solutions to Generalized Vector Quasi-Equilibrium Problems with Discontinuous Mappings

Let X, Y be two finite-dimensional topological vector spaces, Z a Hausdorff topological vector space, K C X and D C Z be two nonempty sets, C be a pointed, closed, and convex cone in Y with int C ≠θ Let S ： K → 2^K and T ： K → 2^D be two multivalued mappings, and φ ： K × D × K → Y be a trifunction. In this paper, we consider the generalized vector quasi-equilibrium problem, which is formulated by finding X∈ K and y∈ T（x） such that x∈ E S（x） and φ（x,y, u） （∈/） -int C for all u ∈ S（x）. We establish an existence result in which T is not supposed to have any continuity property. Our results extend and improve the corresponding results of Cubiotti, Yao and Guo.

含参广义向量均衡问题系统解的通有稳定性

目的对含参广义向量均衡问题系统解的通有稳定性进行研究。方法在支付函数受参数扰动的情况下,通过定义2个系统之间的距离,结合集值映射的上半C-连续性、C-凸性以及Fort定理进行研究。结果与结论证明了(W,ρ)是一个完备度量空间,含参广义向量均衡问题系统解映射是上半连续且具紧值的,以及含参广义向量均衡问题系统解的通有稳定性。

具有控制结构的广义强向量拟均衡问题联立系统

利用锥连续性与不动点定理,研究具有控制结构的广义强向量拟均衡问题联立系统,得到解的存在定理与解集的闭性,并应用于Debreu型强向量均衡问题与广义强向量拟鞍点组的解。

局部FC-一致空间内具有联立广义矢量拟平衡组约束的数学规划(英文)

在局部FC-一致空间内引入和研究了某些新的联立广义矢量拟平衡问题组和具有联立广义矢量拟平衡组约束的数学规划.应用作者在局部FC-一致空间得到的Himmelberg型不动点定理,首先在局部FC-一致空间内对联立广义矢量拟平衡问题组的解证明了某些新的存在性定理.作为应用,对具有联立广义矢量拟平衡组约束的数学规划的解得到了某些新的存在性定理.

局部FC-一致空间内的联立广义矢量拟平衡问题组(英文)

在局部FC-一致空间内引入和研究了某些新的广义矢量拟平衡问题组和联立广义矢量拟平衡问题组.应用KKM型定理和作者在局部FC-一致空间得到的Himmelberg型不动点定理,首先在局部FC-一致空间内对两族集值映象证明了一个新的重合点定理.作为应用,在局部FC-一致空间内得到了广义矢量拟平衡问题组和联立广义矢量拟平衡问题组的解的某些新的存在性定理.这些结果推广了文献中某些已知结果.

伪单调的广义向量拟均衡问题系统

在Hausdorff拓扑线性空间中,引入一类向量伪单调映射,讨论伪单调映射广义向量拟均衡问题系统的有效解与强解;在较弱的锥连续条件下,利用推广的极大元定理,建立两类解之间的联系,证明两类解的存在定理,而且得到解集的紧性。

乘积拓扑矢量空间中的不动点定理和广义矢量平衡问题组

利用零调映象的一个不动点定理,在乘积拓扑矢量空间内得到了某些新的不动点定理,作为应用,在乘积拓扑矢量空间内,对一类广义矢量平衡问题组证明了一些平衡存在性定理,这些定理推广了近期文献中的一些重要的已知结果.

局部FC-一致空间内的广义矢量拟变分包含组和广义矢量拟优化问题组

在没有凸性结构的局部FC-一致空间内,引入和研究了某些新的广义矢量拟变分包含问题组和广义矢量理想(真,帕雷多(Pareto),弱)拟优化问题组.应用KKM型定理和Himmelberg型不动点定理,首先对广义矢量拟变分包含问题组的解,证明了某些新的存在性定理.作为应用,对广义矢量理想(真,帕雷多,弱)拟优化问题组的解也得到了某些新的存在性结果.

乘积FC-空间中新的极大元定理及其对广义混合向量拟平衡问题系统的应用(英文)

在乘积FC-空间中建立一个新的极大元定理,作为应用,获得广义混合向量拟平衡问题系统的解的新的存在定理.