A family f₁,..., fₙ of operators on a complete metric space X is called contractive if there exists a positive λ < 1 such that for any x,y in X we have for some i. Austin conjectured that any commuting contractive family of operators has a common fixed point, and he proved this for the case of two operators. We show that Austin’s conjecture is true for three operators, provided that λ is sufficiently small.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm231-3-2,
author = {Luka Mili\'cevi\'c},
title = {Commuting contractive families},
journal = {Fundamenta Mathematicae},
volume = {228},
year = {2015},
pages = {225-272},
zbl = {1336.54049},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm231-3-2}
}
Luka Milićević. Commuting contractive families. Fundamenta Mathematicae, Tome 228 (2015) pp. 225-272. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm231-3-2/