Hyers-Ulam stability of the first order difference equation generated by\n linear maps

2021/01/06 by Young Woo Nam, Nam, Young Woo
Chemistry · Mathematics · #Chemical Reaction Mechanisms #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Equations Stability Results #Nonlinear Differential Equations Analysis #Primary 39A20 #Secondary 39A45

paper · pdf · doi:10.48550/arxiv.2101.02364

openalex publication_date 2021/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Hyers-Ulam stability of the difference equation z_n+1 = a_nz_n + b_n is\ninvestigated. If \∏_j=1ⁿ|a_j| has subexponential growth rate, then\ndifference equation generated by linear maps has no Hyers-Ulam stability. Other\ncomplementary results are also found where \lim_{n \→ \∞}\n\(\∏_j=1ⁿ|a_j| \)^\(1)/(n) is greater or less than one.\nThese results contain Hyers-Ulam stability of the first order linear difference\nequation with periodic coefficients also.\n

Citations

• Best constant for Hyers–Ulam stability of two step sizes linear difference equations

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