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- W3120852008 abstract "Hyers-Ulam stability of the sequence $ {z_n}_{n in mathbb{N}} $ generated by linear maps is studied. The difference equation $ z_{n+1} = g_n(z_n) $ where $ g_n(z) = a_nz + b_n $ and $ a_n neq 0 $. Hyers-Ulam stability is determined by the the limit of the geometric average of $ a_n $ rather than the type of each linear maps. In particular, if $ prod_{j=1}^{n-1}|a_j| $ is subexponentially increasing sequence, then $ {z_n}_{n in mathbb{N}} $ has no Hyers-Ulam stability. Other complementary results are also established with properties of $ prod_{j=1}^{n-1}|a_j| $. This result contains Hyers-Ulam stability of the first order difference equation with periodic coefficients also." @default.
- W3120852008 created "2021-01-18" @default.
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- W3120852008 date "2021-01-07" @default.
- W3120852008 modified "2023-09-27" @default.
- W3120852008 title "Hyers-Ulam stability of the first order difference equation generated by linear maps" @default.
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