Journal of the
Korean Mathematical Society JKMS

Let $(X,D;\Gamma)$ be a $G$-convex space and $Y$ a Hausdorff space. Then $ \frak A^\kappa_c(X,Y)\subset \frak K \frak O(X,Y)$, where $\frak A^\kappa_c$ is an admissible class (due to Park) and $\frak K \frak O$ denotes the class of multimaps having the KKM property for open-valued multimaps. This new result is used to obtain a KKM type theorem, matching theorems, a fixed point theorem, and a coincidence theorem.

Keywords: KKM principle, generalized convex ($G$-convex) spaces, $\Gamma$-convex subsets, multimaps having the KKM property

MSC numbers: 47H10, 54H25, 55M20