Hyers-Ulam stability of the first order difference equation with average growth rate

2024/02/22 by Young Woo Nam, Nam, Young Woo
Mathematics · #39A20 #39A45 #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Equations Stability Results

paper · pdf · doi:10.48550/arxiv.2402.14271

openalex publication_date 2024/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The first order difference equation induced by the sequence of maps on 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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