Borsuk's antipodal theorem for approachable correspondences

Jean-Marc Bonnisseau (1, 2) , Souhail Chebbi (3) , Pascal Gourdel (1, 2) , Hakim Hammami (2, 4, 5)

1 Axe Economie mathématique et jeux
2 CES - Centre d'économie de la Sorbonne
3 KSU - King Saud University [Riyadh]
4 PSE - Paris School of Economics
5 Ecole Polytechnique de Tunisie

We present an extension of Borsuk's antipodal theorem (on the existence of a zero) to antipodally approachable correspondences defined on bounded, symmetric and balanced domains.

Mots clés: zero of functions; Balanced sets; antipodal preserving functions; antipodal correspondences; approximative selections; antipodally approachable correspondences; zero of functions.

Domaines: Optimisation et contrôle [math.OC]; Economies et finances

Jean-Marc Bonnisseau, Souhail Chebbi, Pascal Gourdel, Hakim Hammami. Borsuk's antipodal theorem for approachable correspondences. Nonlinear Analysis: Theory, Methods and Applications, 2010, 73 (11), pp.3502-3506. ⟨10.1016/j.na.2010.06.076⟩. ⟨halshs-00639803⟩