广义凸空间内的KKM型定理和极小极大不等式及鞍点定理

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。     

New Generalized R-KKM Type Theorems in General Topological Spaces and Applications

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.     

局部凸空间中的不动点定理

证明了局部凸空间中非凸集上的上半连续凝集值映射的一个Ｌｅｒａｙ－Ｓｃｈａｕｄｅｒ型不动点定理,并推广了一些已知的不动点定理。     

Generalized KKM Type Theorems in FC-Spaces with Applications (I)

The class KKM(X,Y) (resp., s-KKM(X,Y,Z)) of set-valued mappings with KKM (resp., s-KKM) property is introduced in FC-spaces without any convexity structure. Some generalized KKM (resp., s-KKM) type theorems are proved in FC-spaces under much weak assumptions. As applications, some new section theorems and coincidence theorems are established in FC-spaces. These theorems generalize many known results in literature. The further applications of these results will be given in a follow-up paper.     

非紧广义凸空间内的拟平衡问题

利用作者得到的一个新的不动点定理,在非紧广义凸空间内证明了拟平衡问题的几个新的平衡存在性定理.这些定理改进和推广了最近文献中许多已知结果.     

一般化凸乘积空间上Fan-Browder型不动点定理及应用

Fan-Browder type fixed point theorems are obtained for non-selfxnaps on noncompact generalized convex product spaces and new existence problems of(partially) maximal element and equilibrium point are discussed as applications of above results.     

广义L-KKM定理及其应用

引入广义L-KKM映射的概念,它包含R-KKM映射,G-KKM映射,H-KKM映射为其特例.在具有(H)性质的拓扑空间中证明了一些新的广义L-KKM型定理,并进一步获得了关于开覆盖的匹配定理.作为广义L-KKM型定理应用,证明了非空交定理.     

H-空间的截口定理重合定理相交定理及其应用*

本文的目的是在H-空间上得出几个截口定理、相交定理和重合定理.作为这些结果的应用,我们研究了H-空间中的极大极小不等式和变分不等式解的存在性问题.本文结果改进和发展了引文[1,3,5,6,8,9,12,14,15,17]中的相应结果.     

H—度量空间中的广义KKM定理及其应用

定义了一个新的空间-H-度量空间并在H-度量空间中,得到了具有有限度量紧闭（开）值的广义H-KKM映像的广义H-KKM定理,这些定理推广了Khamsi和Yuan最近一系列结果。作为应用,还得到有限度量紧闭（开）覆盖的Ky Fan型匹配定理,不动点定理和极小极大不等式,这些结果统一和推广了近期的许多结果。     

KKM type theorems and generalized vector equilibrium problems in noncompact FC-spaces

A new KKM type theorem is first proved under noncompact setting of FC-spaces. As applications of the KKM type theorem, we establish some new existence theorems of solutions for generalized vector equilibrium problems under noncompact setting of FC-spaces. These theorems improve and generalize many known results in literature.     

局部凸拓扑向量空间中的不动点定理

本文在局部凸拓扑向量空间中得到了几个新的不动点定理，推广了［２］中的几个重要结果．     

W-G-F-KKM mapping, intersection theorems and minimax inequalities in FC-space

By using basic KKM theorem, a new matching theorem and some minimax inequalities for set-valued mappings defined on the FC-spaces are proved under very weak assumptions. These results generalized many known results from the recent literature.     

广义Hilbert空间中几何凸函数的几个定理及其应用

研究广义Hilbert空间中几何凸函数的性质,给出一些重要定理,并运用几何凸函数的Jensen不等式建立了三重的双参数Hlder不等式和三重的多参数Minkowski不等式.     

拓扑空间中Fan-Browder映射的连续选择定理及其应用

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．     

拓扑空间上的重合点定理,广义截口定理

首先利用古典的KKM原理证明一般拓扑空间上的KKM型定理并给出一个全交定理,然后作为应用讨论非紧的拓扑空间上重合点定理和广义截口定理.所得结论推广和改进了许多已知结果.     

关于局部凸拓扑向量空间中广义双拟变分不等式

In this paper we investigate generalized bi-quasi-variational inequalities in locally convex topological vector spaces. Motivated and inspired by the recent research work in this field,we establish several existence theorems of solutions for generalized bi-quasi-variational inequalities,which are the extension and improvements of the earlier and recent results obtained previously by many authors including Sun and Ding [18],Chang and Zhang [23] and Zhang [24].     

The matching theorems in G-convex spaces with applications

The purpose of this paper is to establish some new matching theorems in G-convex spaces and, as applications, to obtain some new fixed point theorems, section theorems and a minimax theorem in G-convex spaces. The results presented in this paper improve and generalize the corresponding results in [1], [2], [3], [4], [5], [7], [8], [9], [10], [11] and [12].     

Generalized Bi quasi variational Inequalities in Locally Convex Topological Vector Spaces

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广义凸空间上重合点定理和极大极小不等式

利用已知的KKM型定理,在广义空间上得到若干个新的重合点定理和推广的Fan-Browder型不动点定理,并且讨论了Von Newmann-Sion型极大极小不等式.主要结果改进和推广了文献中的相应结论.