In this paper, we introduce the concept of generalized weak KKM mapping that is more general than many others encountered in the KKM theory. Then, two previous intersection theorems of the author are extended from weak KKM mappings to generalized weak KKM mappings. Applications of these results to set-valued equilibrium problems and minimax inequalities are given in the last two sections.

中文翻译：

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广义弱 KKM 集值映射的交定理在优化中的应用

在本文中，我们介绍了广义弱 KKM 映射的概念，它比 KKM 理论中遇到的许多其他映射更通用。然后，作者之前的两个交集定理从弱 KKM 映射扩展到广义弱 KKM 映射。最后两节给出了这些结果在设定值均衡问题和极小极大不等式中的应用。