Borsuk’s antipodal fixed points theorems for compact or condensing set-valued maps

Altwaijry Najla (najla@ksu.edu.sa), Souhail Chebbi (schebbi@ksu.edu.sa), Hakim Hammami (hakim.hammami@malix.univ-paris1.fr) and Pascal Gourdel (gourdel@univ-paris1.fr)
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Altwaijry Najla: KSU - King Saud University [Riyadh]
Souhail Chebbi: KSU - King Saud University [Riyadh]
Hakim Hammami: College of Telecom and Information, Riyadh
Pascal Gourdel: PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique

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Abstract: We give a generalized version of the well-known Borsuk's antipodal fixed point theorem for a large class of antipodally approachable condensing or compact set-valued maps defined on closed subsets of locally convex topological vector spaces. These results contain corresponding results obtained in the literature for compact set-valued maps with convex values.

Keywords: Borsuk’s antipodal fixed point theorem; approximative selection; antipodally approximable set-valued maps; compact set-valued maps; measure of non-compactness; condensing set-valued maps (search for similar items in EconPapers)
Date: 2018-08-01
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Published in Advances in Nonlinear Analysis, 2018, 7 (3), pp.307-311. ⟨10.1515/anona-2016-0128⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:cesptp:hal-01477126

DOI: 10.1515/anona-2016-0128

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