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1.
In this paper, some new generalized R-KKM type theorems for generalized R-KKM mappings with finitely closed values and with finitely open values are established in noncompact topological spaces without any convexity structure under much weaker assumptions. As applications, some new minimax inequalities, saddle point theorem and equilibrium existence theorem for equilibrium problems with lower and upper bounds are established in general noncompact topological spaces. These theorems unify and generalize many known results in the literature.  相似文献   

2.
Some new coincidence theorems involving admissible set-valued mappings are proved in general noncompact topological spaces. As applications, some new minimax inequalities, section theorem, best approximation theorem, existence theorems of weighted Nash equilibria and Pareto equilibria for multiobjective games are given in general topological spaces.  相似文献   

3.
In this paper, by using a fixed point theorem for expansive set-valued mappings with noncompact and nonconvex domains and ranges in topological spaces due to the author, we first prove a collective fixed point theorem and an existence theorem of equilibrium points for a generalized game. As applications, some new existence theorems of solutions for systems of generalized quasi-variational inclusion problems are established in noncompact topological spaces. Our results are different from known results in the literature.  相似文献   

4.
Some minimax inequalities involving two bifunctions with noncompact and nonconvex domains are first proved in finite continuous topological spaces (in short, FCFC-spaces) without convexity structure. As applications some new Fan–Browder type fixed point theorems for expansive set-valued maps with noncompact and nonconvex domains and ranges are obtained in general topological spaces. These results generalize some known results in the recent literature.  相似文献   

5.
首先,在不具有任何凸性结构的拓扑空间中引入Fan-Browder映射的概念.然后,证明了一个新的关于Fan-Browder映射的连续选择定理,其中定义域是非紧的。值域是不具有任何凸性结构的拓扑空间的子集.作为应用,给出了一些不动点定理、叠合点定理和一个非空交定理.这些新的概念和定理统一和推广了许多已有的结果.  相似文献   

6.
PIAO YONG-JIE 《东北数学》2009,25(3):213-222
A new concept of finitely continuous topological spaces (in short, FC-space) without convexity structure and linear structure was introduced. Some KKM type theorems in noncompact FC-spaces were obtained, and from which, some section theorems and wriational inequality theorems were proved under much weak assumptions. Our results improve and generalize the corresponding conclusions in recent literature.  相似文献   

7.
In this note, we first prove existence theorems for noncompact generalized quasivariational inequalities. As applications, two fixed point theorems for upper or lower semicontinuous multivalued mappings without compact domains are given in locally Hausdorff topological vector spaces. These results generalize or improve corresponding results in the literature.  相似文献   

8.
1IntroductionOneofthemainresultsofequilibriullltheoryforgelleralizedgalllesistileexistellceofmaximalelementsconcerninganirreflexivepreferencecorrespondellcewitllcollvexvalues,openlowersections,definedonacompactconvexsubsetKofRnalldwithvaluesillZap,seen.Chapter7].Duetotheimportallceofapplications,tileresultwasgelleralizedby1flailyauthors,forexample,see[2,5--7,10,13,15-181.Tilelllostoftheseexistellcetheorellisforlllaxilllalelementsandequilibriulllpointsdealwithpreferencecorrespondenceswhichhav…  相似文献   

9.
EQUILIBRIUM PROBLEMS WITH LOWER AND UPPER BOUNDS IN TOPOLOGICAL SPACES   总被引:3,自引:0,他引:3  
1IntroductionLet X be a topological space and f:X×X→R{±∞}be a function.The equilibriumproblem(EP(X,f))is to find x?∈X such thatf(x?,y)≥0,?y∈X.(1)The EP(X,f)(1)includes many fundamental mathematical problems that arise from mechan-ics,engineering,economics,optimization,fixed point,saddle point,variational inequality andcomplementarity problem as special cases.See,for example,[1-4].In1999,Isac,Sehgal and Singh[5]raised the following open problem:given a nonemptyclosed subset K in a…  相似文献   

10.
乘积G-凸空间内的非空交定理和广义矢量平衡问题组   总被引:3,自引:0,他引:3  
利用作在G凸空间内对集值映象簇得到的一个极大元存在性定理,在非紧乘积G空间内,对集值映象簇建立了某些新的非空交定理.作为应用,在非紧乘积G凸空间内,对广义矢量平衡问题组证明了一些平衡存在性定理.这些定理统一、改进和推广了献中一些重要的已知结果.  相似文献   

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