Characterizations of inner product spaces by means of norm one points
| dc.contributor.author | Mendoza Casas, José | |
| dc.contributor.author | Pakhrou, Tijani | |
| dc.date.accessioned | 2023-06-20T09:40:32Z | |
| dc.date.available | 2023-06-20T09:40:32Z | |
| dc.date.issued | 2005 | |
| dc.description.abstract | Let X be a a real normed linear space of dimension at least three, with unit sphere S-X. In this paper we prove that X is an inner product space if and only if every three point subset of S-X has a Chebyshev center in its convex hull. We also give other characterizations expressed in terms of centers of three point subsets of S-X only. We use in these characterizations Chebyshev centers as well as Fermat centers and p-centers. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | D.G.I.C.Y.T. | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/16864 | |
| dc.identifier.issn | 0025-5521 | |
| dc.identifier.officialurl | http://www.mscand.dk/article.php?id=2869 | |
| dc.identifier.relatedurl | http://www.mscand.dk/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/50161 | |
| dc.issue.number | 1 | |
| dc.journal.title | Mathematica Scandinavica | |
| dc.language.iso | eng | |
| dc.page.final | 114 | |
| dc.page.initial | 104 | |
| dc.publisher | Matematisk Institut, Universitetsparken NY Munkegade | |
| dc.relation.projectID | BFM 2001-1284 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.98 | |
| dc.subject.keyword | Chebyshev centers | |
| dc.subject.keyword | characterizations of inner product spaces | |
| dc.subject.ucm | Análisis funcional y teoría de operadores | |
| dc.title | Characterizations of inner product spaces by means of norm one points | |
| dc.type | journal article | |
| dc.volume.number | 97 | |
| dcterms.references | Amir, D., Characterizations of Inner Product Spaces, Birkhäuser Verlag, Basel, 1986. Benítez, C., Fernández, M., and Soriano, L., Location of the 2-centers of three points, Rev. R. Acad. Cienc. Exact. Fís. Natur. Madrid (Esp.) 94 (2000), 515–517. Benítez, C., Fernández, M., and Soriano, L., Weighted p-Centers and the convex hull property, Numer. Funct. Anal. Optim. 23 (2002), 39–45. Benítez, C., Fernández, M., and Soriano, L., Location of the Fermat-Torricelli medians of three points, Trans. Amer. Math. Soc. 304 (2002), 5027–5038. Durier, R., Optimal locations and inner products, J. Math. Anal. Appl. 207 (1997), 220–239. Garkavi, A. L., On the Chebyshev center and the convex hull of a set, Uspekhi Mat. Nauk USSR 19 (1964), 139–145. Klee, V., Circumspheres and inner products, Math. Scand. 8 (1960), 363–370. Mendoza, J., and Pakhrou, T., On some characterizations of inner product spaces, J. Math. Anal. Appl. 282 (2003), 369–382. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 3fdf00ed-ed02-482c-a736-bb87c2753a89 | |
| relation.isAuthorOfPublication.latestForDiscovery | 3fdf00ed-ed02-482c-a736-bb87c2753a89 |
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