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
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.