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KKM and Ky Fan theorems in hyperconvex metric spaces. (English) Zbl 0869.54045
From the text: “In this work, we recall and investigate some basic properties of hyperconvexity. We also discuss Knaster-Kuratowski-Mazurkiewicz mappings (in short KKM-maps) in this setting and prove an analogue of Ky Fan’s fixed point theorem which can be seen as an extension to Brouwer and Schauder’s fixed point theorems. It is to our knowledge the first time that there has been an attempt to prove such theorems in a metric space setting”.

MSC:
54H25Fixed-point and coincidence theorems in topological spaces
47H10Fixed point theorems for nonlinear operators on topological linear spaces