Fixed Point Theory and Applications
Volume 2004 (2004), Issue 2, Pages 107-112

Fixed points of condensing multivalued maps in topological vector spaces

In-Sook Kim

Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea

Received 27 October 2003; Revised 28 January 2004

Copyright © 2004 In-Sook Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.