We obtain a characterization of Ulam stability for the linear difference equation with constant coefficients $$x_{n+p}=a_1x_{n+p-1}+\cdots +a_px_n$$ x n + p = a 1 x n + p - 1 + ⋯ + a p x n in locally convex spaces. Moreover, for the first order linear difference equation we determine the best Ulam constant.

中文翻译：

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局部凸空间中线性差分方程的乌拉姆稳定性

我们获得了具有常系数的线性差分方程的 Ulam 稳定性表征 $$x_{n+p}=a_1x_{n+p-1}+\cdots +a_px_n$$xn + p = a 1 xn + p - 1 + ⋯ + apxn 在局部凸空间中。此外，对于一阶线性差分方程，我们确定最佳 Ulam 常数。