International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 9, Pages 595-612
doi:10.1155/S0161171200004403

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

Abstract

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.