Stability of iterative roots is important in their numerical computation. It is known that under some conditions iterative roots of orientation-preserving self-mappings are both globally stable and locally stable but globally unstable. Although the global instability implies the general global () instability, the local stability does not guarantee the local () stability. In this paper we generally prove the local () stability for iterative roots. For this purpose we need a uniform estimate for the approximation to the conjugation in linearization, which is given by improving the method used for the case.
"Local Stability for Iterative Roots of Orientation-Preserving Self-Mappings on the Interval." J. Appl. Math. 2014 1 - 8, 2014. https://doi.org/10.1155/2014/743032