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Journal of Convex Analysis 15 (2008), No. 1, 055--062
Copyright Heldermann Verlag 2008

The Weighted Fermat-Torricelli Problem and an "Inverse" Problem

Anastasios N. Zachos
University of Patras, Dept. of Mathematics, 26500 Rion, Greece

Gerasimos Zouzoulas
Meintani 25, 117-41 Athens, Greece

We study the weighted Fermat-Torricelli point of spherical, hyperbolic and plane triangles and an inverse weighted Fermat-Torricelli problem. We show that a fundamental application of the inverse weighted Fermat-Torricelli problem is the invariance property of the weighted Fermat-Torricelli point.

Keywords: Fermat-Torricelli point, inverse Fermat-Torricelli problem.

MSC: 51E10, 52A55

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