Fixed points of condensing multivalued maps in topological vector spaces (Q2388416)

The main result of the present paper is that every compact convex set in a complete metric linear space has the fixed point property with respect to admissible multivalued maps. Moreover, the author applies this main result to prove that every pseudocondensing admissible map from a closed convex subset of a complete metric linear space to itself has a fixed point. Finally, the author presents a fixed point theorem for countably condensing admissible maps in Fréchet spaces. These results lead, furthermore, to multivalued versions of the Schauder fixed point theorem in complete metric linear spaces.