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Journal Articles Advances in Nonlinear Analysis Year : 2017

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.

Dates and versions

hal-01477138 , version 1 (27-02-2017)

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Pascal Gourdel, Nadia Mâagli. A convex-valued selection theorem with a non separable Banach space. Advances in Nonlinear Analysis, 2017, 6 (3), ⟨10.1515/anona-2016-0053⟩. ⟨hal-01477138⟩
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