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
zaxos@master.math.upatras.gr
Gerasimos Zouzoulas
Meintani 25, 117-41 Athens, Greece
pantarei@zouzoulas.gr
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
[ Fulltext-pdf (119 KB)] for subscribers only.