Let T be a bounded linear operator acting on a Banach space X. We obtain some results on Ulam stability for the linear difference equation \(x_{n+1}=Tx_n+a_n\) associated with an iterative process for the linear equation \(x-Tx=y.\) As applications, we get some stability results for the case when X is a finite-dimensional space and for the case when T is a Fredholm operator.

中文翻译：

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逐次逼近方程的Ulam稳定性

令T为作用于Banach空间X的有界线性算子。对于线性差分方程\（x_Tx = y。\）的迭代过程，我们获得了线性差分方程\（x_ {n + 1} = Tx_n + a_n \）的Ulam稳定性的一些结果作为应用，我们得到对于X是有限维空间的情况和对于T是Fredholm算符的情况，会产生一些稳定性。