International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 9, Pages 595-612

Fixed points and selections of set-valued maps on spaces with convexity

Peter Saveliev

Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana 61801, IL, USA

Received 22 November 1999

Copyright © 2000 Peter Saveliev. 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.


We provide theorems extending both Kakutani and Browder fixed points theorems for multivalued maps on topological vector spaces, as well as some selection theorems. For this purpose we introduce convex structures more general than those of locally convex and non-locally convex topological vector spaces or generalized convexity structures due to Michael, van de Vel, and Horvath.