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April 10, 2015 By

The Ky Fan fixed point theorem on star-shaped domains

C. R. Math. Rep. Acad. Sci. Canada Vol. 27, (4), 2005 pp. 97–100

December 30, 2005

Hichem Ben-El Mechaiekh, Department of Mathematics, Brock University, St. Catharines, Ontario, L2S 3A1; email: hmechaie@brocku.ca

Abstract/Résumé:

We extend the Ky Fan fixed point theorem for a set-valued map with convex non-empty values and open fibers defined on a star-shaped compact subset in a topological vector space. The proof is elementary and based on a matching theorem of Ky Fan for open covers of convex sets.

Nous généralisons le théorème de point fixe de Ky Fan pour une application à valeurs d’ensembles convexes non-vides et à images inverses ouvertes définie sur un domaine compact et étoilé dans un espace vectoriel topologique. La preuve est élémentaire et se base sur un théorème de “matching” de Ky Fan pour les recouvrements ouverts d’ensembles convexes.

Keywords:
AMS Subject Classification: Fixed-point theorems 47H10

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