A convex-valued selection theorem with a non separable Banach space
Journal article: 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.
Author(s)
Pascal Gourdel, Nadia Mâagli
Journal
- Advances in Nonlinear Analysis
Date of publication
- 2017
Keywords
- Closed valued correspondence
- Lower semicontinuous correspondence
- Continuous selections
- Barycentric coordinates
- Separable Banach spaces
- Finite dimensional convex values
URL of the HAL notice
Version
- 1
Volume
- 6