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

作者：Gourdel Pascal^*; Maagli Nadia

来源：Advances in Nonlinear Analysis, 2018, 7(2): 197-209.

DOI：10.1515/anona-2016-0053

• Barycentric coordinates
• continuous selections
• lower semicontinuous correspondence
• closed-valued correspondence
• finite-dimensional convex values
• separable Banach spaces

In the spirit of Michael's selection theorem [6, Theorem 3.1'''], we consider a nonempty convex-valued lower semicontinuous correspondence phi : X -> 2(Y). We prove that if phi 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.

• 出版日期2018-5