Local C1 stability versus global C1 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 C0 stable in both the local sense and the global sense. In this paper we discuss the C1 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 C1 stable but globally C1 unstable.