Location of the Fermat-Torricelli medians of three points

DOI10.1090/S0002-9947-02-03113-6zbMath1030.46009MaRDI QIDQ3151265

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Publication date: 7 October 2002

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

normed spaceFermat problemcharacterization of inner product spaceFermat-Torricelli median

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Characterizations of Hilbert spaces (46C15)

Related Items (10)

Two new examples of sets without medians and centers ⋮ Reconstruction of norm by geometry of minimal networks ⋮ Existence of Lipschitz selections of the Steiner map ⋮ The Fermat-Torricelli theorem in convex geometry ⋮ Location problem and inner product spaces ⋮ Correlation between the norm and the geometry of minimal networks ⋮ Averaging the \(k\) largest distances among \(n\): \(k\)-centra in Banach spaces ⋮ The type of minimal branching geodesics defines the norm in a normed space ⋮ The Fermat--Torricelli problem in normed planes and spaces ⋮ Middle points, medians and inner products

Cites Work

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• On the line segments of a convex surface in \(E_3\)
• Geometric methods and optimization problems
• The Fermat-Weber problem and inner product spaces
• Steiner minimal trees
• Characterizations of inner product spaces
• Circumspheres and Inner Products.
• Convex hull properties in location theory
• WEIGHTEDp-CENTERS AND THE CONVEX HULL PROPERTY
• ON A NEW PROOF OF DURIER'S THEOREM
• Location Theory, Dominance, and Convexity

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