拓扑空间中新的广义L-KKM型定理及其应用

New Generalized $L$-KKM Type Theorems in Topological Spaces with Applications

中文关键词:  广义L-KKM映射  有限闭值  有限开值  不动点  平衡问题.

英文关键词:generalized $L$-KKM mapping  finitely closed valued  finitely open valued  fixed point  equilibrium problem.

中文摘要:

      本文在没有任何凸结构的拓扑空间中建立了关于有限开值和有限闭值的新的广义L-KKM型定理.作为应用,在适当的条件下得到了匹配定理、不动点定理和上下界平衡问题解的存在定理,这些定理统一和推广了最近文献中的相关定理.

英文摘要:

      In this paper, some new generalized $L$-KKM type theorems with finitely open values and with finitely closed values are established without any convexity structure in topological spaces. As applications, some new matching theorem, fixed point theorem and existence theorem of equilibrium problem with lower and upper bounds are also given under some suitable conditions. These theorems presented in this paper unify and generalize some corresponding known results in recent literatures.