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

PDF(click to download): The Ky Fan fixed point theorem on star-shaped domains

S. Reich / A.J. Zaslavki

Abstract/Résumé:

No abstract available but the full text pdf may be downloaded at the title link below.

Keywords: contractive mapping, fixed point set, generic property, nonexpansive mapping, uniform space

AMS Subject Classification: Nonexpansive mappings; and their generalizations (ultimately compact mappings; measures of noncompactness and condensing mappings; $A$-proper mappings; $K$-set contractions; etc.), Fixed-point theorems, 47H09, 47H10, 58F99

PDF(click to download): Almost all nonexpansive mappings are contractive

S.L. Singh / S.N. Mishra

Abstract/Résumé:

No abstract available but the full text pdf may be downloaded at the title link below.

Keywords: Coincidence point, fixed point, multi-valued maps, weak compatibility

AMS Subject Classification: Fixed-point theorems, Set-valued maps, Fixed-point and coincidence theorems 47H10, 54C60, 54H25

PDF(click to download): Some remarks on coincidences and fixed points