We show that the use of Brouwer fixed point theorem in Mironescu-Panaitopol's approach to the existence of a triangle with prescribed interior bisector lengths can be replaced by that of Banach fixed point theorem followed by an elementary limiting argument.
Publié le : 2010-04-15
Classification:
three bisectors problem,
Brouwer fixed point theorem,
Banach fixed point theorem,
51M04,
47H10,
01A55,
01A60
@article{1274896209,
author = {Dinca, George and Mawhin, Jean},
title = {A constructive fixed point approach to the existence of a triangle with prescribed angle bisector lengths},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {17},
number = {1},
year = {2010},
pages = { 333-341},
language = {en},
url = {http://dml.mathdoc.fr/item/1274896209}
}
Dinca, George; Mawhin, Jean. A constructive fixed point approach to the existence of a triangle with prescribed angle bisector lengths. Bull. Belg. Math. Soc. Simon Stevin, Tome 17 (2010) no. 1, pp. 333-341. http://gdmltest.u-ga.fr/item/1274896209/