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Global \(C^{0}\) and local \(C^{1}\) stability of iterative roots for monotonic functions defined on a compact interval, as well as global \(C^{1}\) instability under some assumptions, are well-known facts. In this paper, we investigate the stability of iterative roots for piecewise monotonic functions with nonmonotonicity height equal to 1. We prove the roots are \(C^{1}\) locally stable and \(C^{0}\) global stable with the same extension.

Stability for iterative roots of piecewise monotonic functions