A convex-valued selection theorem with a non separable Banach space

Abstract : In the spirit of Michael selection theorem (Theorem 3.1′′′, 1956), we consider a nonempty convex valued lower semicontinuous correspondence φ : X → 2^Y . We prove that if φ has either closed or finite dimensional images, then there admits a continuous single valued selection, where X is a metric space and Y is a Banach space. We provide a geometric and constructive proof of our main result based on the concept of peeling introduced in this paper.
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Article dans une revue
Advances in Nonlinear Analysis, 2017, forthcoming
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https://hal.archives-ouvertes.fr/hal-01477138
Contributeur : Pascal Gourdel <>
Soumis le : lundi 27 février 2017 - 09:10:19
Dernière modification le : mardi 28 février 2017 - 01:06:03

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  • HAL Id : hal-01477138, version 1

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Pascal Gourdel, Nadia Mâagli. A convex-valued selection theorem with a non separable Banach space. Advances in Nonlinear Analysis, 2017, forthcoming. <hal-01477138>

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