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Hyers-Ulam stability of the first order difference equation generated by linear maps (2101.02364v6)
Published 7 Jan 2021 in math.DS
Abstract: Hyers-Ulam stability of the difference equation $ z_{n+1} = a_nz_n + b_n $ is investigated. If $ \prod_{j=1}{n}|a_j| $ has subexponential growth rate, then difference equation generated by linear maps has no Hyers-Ulam stability. Other complementary results are also found where $ \lim_{n \rightarrow \infty} \left(\prod_{j=1}{n}|a_j| \right){\frac{1}{n}} $ is greater or less than one. These results contain Hyers-Ulam stability of the first order linear difference equation with periodic coefficients also.