On finitely many fixed points
Let C be the finite union of closed convex sets in a complete metrisable locally convex space. If f: C → C with f(C) compact, then f can be approximated by a map g: C → C which has only a finite number of fixed points. This result, which is a generalization of the result of Baillon and Rallis, is proved in this paper.
Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 167-170