Commuting contractive families
Fundamenta Mathematicae, Tome 231 (2015) no. 3, pp. 225-272
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
A family $f_1,\ldots ,f_n$ of operators on a complete metric space $X$ is called contractive if there exists a positive $\lambda 1$ such that for any $x,y$ in $X$ we have $d(f_i(x),f_i(y)) \leq \lambda d(x,y)$ 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 $\lambda $ is sufficiently small.
Keywords:
family ldots operators complete metric space called contractive there exists positive lambda have x leq lambda austin conjectured commuting contractive family operators has common fixed point proved operators austins conjecture three operators provided lambda sufficiently small
Affiliations des auteurs :
Luka Milićević 1
@article{10_4064_fm231_3_2,
author = {Luka Mili\'cevi\'c},
title = {Commuting contractive families},
journal = {Fundamenta Mathematicae},
pages = {225--272},
publisher = {mathdoc},
volume = {231},
number = {3},
year = {2015},
doi = {10.4064/fm231-3-2},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm231-3-2/}
}
Luka Milićević. Commuting contractive families. Fundamenta Mathematicae, Tome 231 (2015) no. 3, pp. 225-272. doi: 10.4064/fm231-3-2
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