Mendoza Casas, Jose and Pakhrou, Tijani (2005) Characterizations of inner product spaces by means of norm one points. Mathematica Scandinavica, 97 (1). pp. 104-114. ISSN 0025-5521
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Official URL: http://www.mscand.dk/article.php?id=2869
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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Chebyshev centers; characterizations of inner product spaces |
| Subjects: | Sciences > Mathematics > Functional analysis and Operator theory |
| ID Code: | 16864 |
| 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. |
| Deposited On: | 25 Oct 2012 10:38 |
| Last Modified: | 25 Oct 2012 10:38 |
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