Subcommuting and comparable iterative roots of order preserving homeomorphisms

Abstract

It is known that the iterative roots of continuous functions are not necessarily unique, if it exist. In this note, by introducing the set of points of coincidence, we study the iterative roots of order preserving homeomorphisms. In particular, we prove a characterization of identical iterative roots of an order preserving homeomorphism using the points of coincidence of functions. 2019 King Saud University & Saudi Association for Mathematical Sciences