Location problem and inner product spaces
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http://hdl.handle.net/10045/135767
Title: | Location problem and inner product spaces |
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Authors: | Pakhrou, Tijani |
Research Group/s: | Curvas Alpha-Densas. Análisis y Geometría Local |
Center, Department or Service: | Universidad de Alicante. Departamento de Matemáticas |
Keywords: | Optimal location | Chebyshev centers | Medians | Inner product spaces |
Issue Date: | 4-Jul-2023 |
Publisher: | Elsevier |
Citation: | Journal of Functional Analysis. 2023, 285(8): 110078. https://doi.org/10.1016/j.jfa.2023.110078 |
Abstract: | In this work we solve a problem that has been open for more than 110 years (see [21]). We prove that a real normed space (X, || · ||) of dimension greater than or equal to three is an inner product space if and only if, for every three points a1, a2, a3 ∈ X, the set of points at which the function x ∈ X → γ(||x − a1||, ||x − a2||, ||x − a3||) attains its minimum, intersects the convex hull of these three points, where γ is a symmetric monotone norm on R3. |
URI: | http://hdl.handle.net/10045/135767 |
ISSN: | 0022-1236 (Print) | 1096-0783 (Online) |
DOI: | 10.1016/j.jfa.2023.110078 |
Language: | eng |
Type: | info:eu-repo/semantics/article |
Rights: | © 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). |
Peer Review: | si |
Publisher version: | https://doi.org/10.1016/j.jfa.2023.110078 |
Appears in Collections: | INV - CADAGL - Artículos de Revistas INV - GAM - Artículos de Revistas |
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Pakhrou_2023_JFunctAnal.pdf | 383,85 kB | Adobe PDF | Open Preview | |
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