A convex-valued selection theorem with a non-separable Banach space
In the spirit of Michael’s selection theorem [6, Theorem 3.1”’], we consider a nonempty convex-valued lower semicontinuous correspondence φ:X→2Y{\varphi:X\to 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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2018-05-01
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| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2016-0053 |
| Summary: | In the spirit of Michael’s selection theorem [6, Theorem 3.1”’], we consider a nonempty convex-valued lower semicontinuous correspondence
φ:X→2Y{\varphi:X\to 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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| ISSN: | 2191-9496 2191-950X |