We are excited to announce that the repository will soon undergo an upgrade, featuring a new look and feel along with several enhanced features to improve your experience. Please be on the lookout for further updates and announcements regarding the launch date. We appreciate your support and look forward to unveiling the improved platform soon.
dc.contributor.author | Messerschmidt, Miek![]() |
|
dc.date.accessioned | 2019-05-28T11:57:20Z | |
dc.date.issued | 2019-03 | |
dc.description.abstract | We prove that any correspondence (multi-function) mapping a metric space into a Banach space that satisfies a certain pointwise Lipschitz condition, always has a continuous selection that is pointwise Lipschitz on a dense set of its domain. We apply our selection theorem to demonstrate a slight improvement to a well-known version of the classical Bartle-Graves Theorem: Any continuous linear surjection between infinite dimensional Banach spaces has a positively homogeneous continuous right inverse that is pointwise Lipschitz on a dense meager set of its domain. An example devised by Aharoni and Lindenstrauss shows that our pointwise Lipschitz selection theorem is in some sense optimal: It is impossible to improve our pointwise Lipschitz selection theorem to one that yields a selection that is pointwise Lipschitz on the whole of its domain in general. | en_ZA |
dc.description.department | Mathematics and Applied Mathematics | en_ZA |
dc.description.embargo | 2020-03-01 | |
dc.description.librarian | hj2019 | en_ZA |
dc.description.sponsorship | The Claude Leon Foundation | en_ZA |
dc.description.uri | https://link.springer.com/journal/11228 | en_ZA |
dc.identifier.citation | Messerschmidt, M. A Pointwise Lipschitz Selection Theorem. Set-Valued and Variational Analysis (2019) 27: 223-240. https://doi.org/10.1007/s11228-017-0455-2. | en_ZA |
dc.identifier.issn | 1877-0533 (print) | |
dc.identifier.issn | 1877-0541 (online) | |
dc.identifier.other | 10.1007/s11228-017-0455-2 | |
dc.identifier.uri | http://hdl.handle.net/2263/69220 | |
dc.language.iso | en | en_ZA |
dc.publisher | Springer | en_ZA |
dc.rights | © Springer Science+Business Media B.V. 2017. The original publication is available at https://link.springer.com/journal/11228. | en_ZA |
dc.subject | Selection theorem | en_ZA |
dc.subject | Pointwise Lipschitz map | en_ZA |
dc.subject | Bartle-Graves theorem | en_ZA |
dc.title | A pointwise Lipschitz selection theorem | en_ZA |
dc.type | Postprint Article | en_ZA |