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1.
System of Generalized Vector Quasi-Equilibrium Problems in Locally FC-Spaces   总被引:11,自引:0,他引:11  
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.  相似文献
2.
乘积拓扑空间内的重合点组定理及应用(Ⅰ)   总被引:9,自引:1,他引:8  
丁协平 《应用数学和力学》2005,26(12):1401-1408
首先引入了无凸性结构的有限连续拓扑空间(简称FC_空间)新概念.其次在FC_空间内建立了一个新的连续选择定理.应用此定理,在很弱的假设下,对定义在非紧FC_空间的乘积空间上的两个集值映射簇证明了某些新的重合点定理.这些结果推广了最近文献中的许多已知结果.某些应用将在后继文章中给出.  相似文献
3.
丁协平 《数学学报》2004,47(4):711-722
本文在非紧G-凸空间内对具有有限闭值和有限开值的G-KKM,广义G-KKM和广义S-KKM映象建立了某些新的KKM型定理。应用这些KKM型定理,在G-凸空间内得到了新的 Ky Fan型极小极大不等式和鞍点定理。这些结论推广了最近文献中的许多已有结果。  相似文献
4.
王学平  屈小兵 《数学学报》2006,49(5):1171-118
本文首先引入连续并既约元(是并既约元但不是完全并既约元的元)的概念,并讨论了它的性质,然后应用连续并既约元的性质去刻画完备Brouwer格上无限Fuzzy关系方程A☉X=b的解集(其中A=(aj)j∈J和b已知,b为连续并既约元,X= (xj)j∈JT未知,“☉”表示“sup-inf”,J为无限集):给出了方程存在可达解与不可达解的充要条件及可达解与不可达解的一些性质,进一步刻画了方程的解集.  相似文献
5.
By applying a maximal element theorem on product FC-space due to author, some new equilibrium existence theorems for generalized games with fuzzy constraint corre- spondences 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.  相似文献
6.
In this paper, we study the class of mixed variational-like inequalities in reflexive Banach spaces. By applying a minimax inequality due to the author, some existence and uniqueness theorems for solutions of mixed variational-like inequalities are proved. Next, by applying the auxiliary problem technique, we suggest an innovative iterative algorithm to compute approximate solutions of the mixed variational-like inequality. Finally, convergence criteria are also discussed. This research was supported by NSF, Sichman Education Department of China, Projects 2003A081 and SZD0406. The author expresses his sincere thanks to Professor H.P. Benson and the anonymous referees for careful comments leading to the present version of this paper.  相似文献
7.
同向单形到欧氏空间的等距嵌入及其应用   总被引:3,自引:0,他引:3       下载免费PDF全文
该文利用矩阵的方法, 获得了两个同向的 n 维单形同时等距嵌入 En 维欧氏空间的一个充分必要条件是: 对于预给(n+1)2个距离,满足一组具有行列式形式的不等式组det(△k)<0, 由此可以得到两组等数量的有限点集合到 En 维欧氏空间中等长嵌入的一个充分必要条件. 然后利用杨路和张景中引进的代数方法, 应用广义等距嵌入定理, 提出了关于两组两个完全同向的 n 维单形“广义度量加”的概念, 并且证明了涉及“广义度量加”的一个几何不等式, 它推广了杨路和张景中关于Alexander猜想的结果. 同时我们将杨路和张景中关于Neuberg-Pedoe不等式的高维推广形式推广到两组两个完全同向的 n 维单形中, 获得了涉及四个单形的一类几何不等式, 它们蕴含近期诸多文献的主要结果.  相似文献
8.
Generalized KKM type theorems in FC-spaces with applications (II)   总被引:2,自引:0,他引:2  
This paper is a continuum of the preceding paper of author. By applying a coincidence theorem in noncompact FC-space without any convexity structure due to author, a new KKM type theorem is first proved under noncompact setting of FC-spaces. The equivalent relation between the coincidence theorem and the KKM type theorem is also established. As applications of the KKM type theorem, we establish some new existence theorems of solutions for three classes of generalized vector equilibrium problems under noncompact setting of FC-spaces. These theorems improve and generalize many known results in literature.  相似文献
9.
丁协平 《应用数学和力学》2007,28(12):1392-1399
首先在没有凸性结构的局部FC-一致空间内引入了非紧性测度和凝聚集值映象概念.在局部FC-一致空间内对涉及凝聚集值映象的集值映象族证明了新的极大元存在性定理.作为应用,在局部FC-一致空间内对涉及凝聚集值映象的广义对策建立了某些新的平衡存在性定理.这些结果改进和推广了文献中的某些已知结果到局部FC-一致空间.对广义矢量拟平衡组的进一步应用,我们将在文(Ⅱ)中给出.  相似文献
10.
Some new continuous selection theorems are first proved in noncompact topological spaces. As applications, some new collectively fixed point theorems and coincidence theorems for two families of set-valued mappings defined on product space of noncompact topological spaces are obtained under very weak assumptions. These results generalize many known results in recent literature.  相似文献
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