具有平均增长率的一阶差分方程的Hyers-Ulam稳定性
Hyers-Ulam stability of the first order difference equation with average growth rate
AI总结：
本文研究一阶差分方程的Hyers-Ulam稳定性，证明增长率几何平均极限收敛且不为1时方程稳定，并揭示平均增长率为（预）周期时即使各周期增长率均小于1也不稳定。
摘要：
由$\mathbb{C}$上映射序列导出的一阶差分方程具有Hyers-Ulam稳定性，其中增长率几何平均的极限收敛且不等于1。%平均增长率是映射收缩或扩张常数的推广。我们证明，当平均增长率为（预）周期时，即使每个周期增长率严格小于1，也不具有Hyers-Ulam稳定性。给出了由含收缩映射和扩张映射的时间依赖映射生成的差分方程的例子。
英文摘要：
The first order difference equation induced by the sequence of maps on $ \mathbb{C} $ has Hyers-Ulam stability where the limit of the geometric average of growth rate is convergent and not equal to one. %The average growth rate is a generalization of contracting or expanding constant of maps. We show no Hyers-Ulam stability where the average growth rate is (pre)periodic even though each periodic growth rate is strictly less than one. Examples of difference equation generated by time dependent maps which contains contracting maps and expanding maps are given.
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