拓扑空间内的广义R-KKM型定理及其应用(英文)

Generalized R-KKMType Theorems in Topological Spaces and Applications

在没有任何凸性结构的非紧拓扑空间内对具有(转移)紧闭值的广义R-KKM映射建立了某些新的广义R-KKM型定理.作为应用,在拓扑空间内得到了某些极小极大不等式,鞍点定理和具有下和上界的平衡问题的平衡存在性定理.这些定理推广了最近文献中某些已知结果.

Some new generalized R- KKM type theorems for generalized R- KKM mappings with （transfer） compactly closed values are established in noncompact topological spaces without any convexity structure. As applications, some minimax inequalities, saddle point theorems and equilibrium existence theorems for equilibrium problems with lower and upper bounds are obtained in topological spaces. These results generalize some known results in recent literatures.