【摘要】 L-凸空间推广了G-凸空间,广义H-空间,超凸度量空间等一大批凸空间,该空间的探讨为非线性分析问题的研究提供了广泛而重要的背景.通过在L-凸空间的非空子集上导出一类新的广义S-LKKM映射,在非紧的条件下建立了L-凸空间的广义LKKM定理和广义S-LKKM定理,这些定理改进和推广了近期文献[1-4]的许多重要结果.作为应用,可以得到L-凸空间中极大极小不等式和鞍点定理;进一步,还可以探讨不动点定理和截口定理,极大元定理和抽象经济的平衡存在性等问题.更多还原

【Abstract】 L-convex spaces generalize many convex spaces,such as G-convex spaces,generalized H-spaces and hyperconvex metric spaces.The study of L-convex spaces provides wide and important background for the research of nonlinear-analysis problems.In this paper,new classes of generalized S-LKKM mappings in a nonempty subset of an L-convex space are derived.New generalized LKKM and generalized S-LKKM theorems,which improve and generalize many important results in references \,are established under the noncompact setting.As a application of the above results,some minimax inequalities and saddle point theorems can be obtained.In addition,fixed point theorems and section theorems,maximal element theorems and the existence theorems of equilibrium for abstract economies can also be discussed.更多还原