Commuting contractive families

Luka Milićević. "Commuting contractive families." Fundamenta Mathematicae 231.3 (2015): 225-272. <http://eudml.org/doc/282968>.

@article{LukaMilićević2015,
abstract = {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 $d(f_i(x),f_i(y)) ≤ λ d(x,y)$ 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.},
author = {Luka Milićević},
journal = {Fundamenta Mathematicae},
keywords = {contraction mappings; complete metric spaces},
language = {eng},
number = {3},
pages = {225-272},
title = {Commuting contractive families},
url = {http://eudml.org/doc/282968},
volume = {231},
year = {2015},
}

TY - JOUR
AU - Luka Milićević
TI - Commuting contractive families
JO - Fundamenta Mathematicae
PY - 2015
VL - 231
IS - 3
SP - 225
EP - 272
AB - 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 $d(f_i(x),f_i(y)) ≤ λ d(x,y)$ 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.
LA - eng
KW - contraction mappings; complete metric spaces
UR - http://eudml.org/doc/282968
ER -