We introduce and study the Hyers–Ulam stability (HUS) of a Cayley quantum (q-difference) equation of first order, where the constant coefficient is allowed to range over the complex numbers. In particular, if this coefficient is non-zero, then the quantum equation has Hyers–Ulam stability for certain values of the Cayley parameter, and we establish the best (minimal) HUS constant in terms of the coefficient only, independent of q and the Cayley parameter. If the Cayley parameter equals one half, then there is no Hyers–Ulam stability for any coefficient value in the complex plane.

中文翻译：

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量子方程的Hyers–Ulam稳定性

我们介绍和研究一阶Cayley量子（q-差分）方程的Hyers-Ulam稳定性（HUS），其中常数系数可以在复数范围内变化。特别是，如果该系数不为零，则对于某些Cayley参数值，该量子方程具有Hyers-Ulam稳定性，并且我们仅根据系数来建立最佳（最​​小）HUS常数，与q和m无关。Cayley参数。如果Cayley参数等于一半，则复平面上任何系数值都没有Hyers-Ulam稳定性。