Local stability versus global unstability for iterative roots

Stability of iterative roots is important in the numerical computation of iterative roots. Known results show that under some conditions iterative roots of strictly monotonic self-mappings are C 0 stable in both the local sense and the global sense. In this paper we discuss the C 1 stability for iterative roots of strictly increasing self-mappings on a compact interval between two fixed points. We prove that those iterative roots are locally C 1 stable but globally C 1 unstable.