Abstract
In this paper, a new KKM theorem is established in L-convex spaces. As applications, a Ky Fan matching theorem for compactly open covers, a Fan–Browder coincidence theorem, a Fan–Browder fixed point theorem and a maximal element theorem are obtained in L-convex spaces. These theorems unify, improve and generalize some recent results in the references therein. Finally, the equilibrium existence theorems for abstract economies and qualitative games in L-convex spaces are yielded.
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