可交换的收缩族
Commuting Contractive Families
摘要：
完全度量空间$X$上的算子族$f_1,...,f_n$称为压缩的，如果存在正的$λ< 1$使得对于$X$中的任何$x,y$，我们对于某个$i$有$d(f_i(x),f_i(y)) \leq λd(x,y)$。奥斯汀证明，任何交换压缩家庭的运营商有一个共同的不动点，他证明了这两个运营商的情况下。本文的目的是证明Austin猜想对三个算子成立，只要$λ$足够小.
英文摘要：
A family $f_1,...,f_n$ 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 $d(f_i(x),f_i(y)) \leq λd(x,y)$ 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. Our aim in this paper is to show that Austin's conjecture is true for three operators, provided that $λ$ is sufficiently small.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
