Many applications using discrete dynamics employ either -difference equations or -difference equations. In this work, we introduce and study the Hyers–Ulam stability (HUS) of a quantum (-difference) equation of Euler type. In particular, we show a direct connection between quantum equations of Euler type and -difference equations of constant step size with constant coefficients and an arbitrary integer order. For equation orders greater than two, the -difference results extend first-order and second-order results found in the literature, and the Euler-type -difference results are completely novel for any order. In many cases, the best HUS constant is found.

中文翻译：

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Euler型量子方程的Hyers-Ulam稳定性

使用离散动力学的许多应用都采用-差分方程或-差分方程。在这项工作中，我们介绍并研究了Euler型量子（-差）方程的Hyers-Ulam稳定性（HUS）。特别地，我们展示了欧拉类型的量子方程与具有恒定系数和任意整数阶的恒定步长的-差分方程之间的直接联系。对于大于两个方程订单，-差导致延伸的一阶和二阶的结果在文献中找到，和欧拉型-差结果对于任何顺序完全新颖的。在许多情况下，可以找到最佳的HUS常数。