Palanivel, R.Murugan, V.2026-02-042023Aequationes Mathematicae, 2023, 97, 3, pp. 575-59519054https://doi.org/10.1007/s00010-022-00935-whttps://idr.nitk.ac.in/handle/123456789/21886The Hyers-Ulam stability of the iterative equation fn= F for continuous functions F was studied under the assumptions that F is a homeomorphism on its range, and the equation has stability on its range. It is important to study the stability of the equation for homeomorphisms on intervals. In this paper, theorems on stability are obtained using the properties of monotonic approximate solutions. The method is based on the stability of two derived iterative equations. © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.HomeomorphismHyers-Ulam stabilityIterative equationIterative root