We obtain a result on Ulam stability and on the best Ulam constant for the linear difference equation \(x_{n+3}=ax_{n+2}+bx_{n+1}+c x_n,\)\(a,b,c \in \mathbb {K}\), where \(\mathbb {K}\) is one of the fields \(\mathbb {R}\) or \(\mathbb {C},\) and \((x_n)_{n\ge 0}\) is a sequence in a Banach space X over the field \(\mathbb {K}\).

中文翻译：

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Banach空间中一类三阶线性差分方程的Ulam稳定性。

我们获得乌拉姆稳定性和最佳乌拉姆常数线性差分方程的结果\（X_ {N + 3} = ax_ {N + 2} + bx_ {N + 1} + C x_n，\）\（一， b，c \ in \ mathbb {K} \），其中\（\ mathbb {K} \）是字段\（\ mathbb {R} \）或\（\ mathbb {C}，\）和\ （（x_n）_ {n \ ge 0} \）是Banach空间X中字段\（\ mathbb {K} \）上的序列。