Stability for iterative roots of piecewise monotonic functions

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.