On the Vietoris semicontinuity property of the $L_p$ balls at $p=1$ and an application
| dc.authorid | 0000-0002-3911-2304 | tr |
| dc.contributor.author | Hüseyin, Anar | |
| dc.date.accessioned | 2023-09-22T10:56:20Z | |
| dc.date.available | 2023-09-22T10:56:20Z | |
| dc.date.issued | 19.07.2023 | tr |
| dc.department | Fen Fakültesi | tr |
| dc.description.abstract | In this paper the Vietoris right lower semicontinuity at $p=1$ of the set valued map $p\rightarrow B_{\Omega,\mathcal{X},p}(r)$, $p\in [1,\infty]$, is discussed where $B_{\Omega,\mathcal{X},p}(r)$ is the closed ball of the space $L_{p}(\Omega,\Sigma,\mu; \mathcal{X})$ centered at the origin with radius $r$, $(\Omega,\Sigma,\mu)$ is a finite and positive measure space, $\mathcal{X}$ is a separable Banach space. It is proved that the considered set valued map is Vietoris right lower semicontinuous at $p=1$. Introducing additional geometric constraints on the functions from the ball $B_{\Omega,\mathcal{X},1}(r)$, a property which is close to the Hausdorff right lower semicontinuity, is derived. An application of the obtained result to the set of integrable outputs of the input-output system described by the Urysohn type integral operator is studied. | tr |
| dc.identifier.citation | Huseyin, A. On the Vietoris semicontinuity property of the 𝐿𝑝 balls at 𝑝=1 and an application. Arch. Math. 121, 171–182 (2023). https://doi.org/10.1007/s00013-023-01881-y | tr |
| dc.identifier.doi | 10.1007/s00013-023-01881-y | en_US |
| dc.identifier.endpage | 182 | tr |
| dc.identifier.issue | 2 | tr |
| dc.identifier.scopus | 2-s2.0-85165207779 | en_US |
| dc.identifier.scopusquality | N/A | |
| dc.identifier.startpage | 171 | tr |
| dc.identifier.uri | https://link.springer.com/article/10.1007/s00013-023-01881-y | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12418/14129 | |
| dc.identifier.volume | 121 | tr |
| dc.identifier.wos | WOS:001032567300001 | en_US |
| dc.identifier.wosquality | Q3 | |
| dc.indekslendigikaynak | Web of Science | en_US |
| dc.indekslendigikaynak | Scopus | en_US |
| dc.language.iso | en | en_US |
| dc.publisher | Birkhauser Verlag | tr |
| dc.relation.ispartof | Archiv der Mathematik | en_US |
| dc.relation.publicationcategory | Uluslararası Hakemli Dergide Makale - Kurum Öğretim Elemanı | tr |
| dc.rights | info:eu-repo/semantics/closedAccess | tr |
| dc.subject | Vietoris semicontinuity, set valued map, Urysohn integral operator, input-output system | tr |
| dc.title | On the Vietoris semicontinuity property of the $L_p$ balls at $p=1$ and an application | en_US |
| dc.type | Article | en_US |
