Fixed Point Theory and Applications
Volume 2004 (2004), Issue 2, Pages 107-112
doi:10.1155/S1687182004310041

Fixed points of condensing multivalued maps in topological vector spaces

Abstract

With the aid of the simplicial approximation property, we show that every admissible multivalued map from a compact convex subset of a complete metric linear space into itself has a fixed point. From this fact we deduce the fixed point property of a closed convex set with respect to pseudocondensing admissible maps.