We prove that an iterated function system of similarities on $\mathbb{R}$ satisfies the weak separation condition and has interval as its self-similar set stronger generalized finite type condition. It is unknown if assumption necessary.

The Kuo condition and the second are known as criteria for an r-jet to be V-sufficient in Cr mappings Cr+1 mappings, respectively. In [2] we considered notions of V-sufficiency jets these conditions relative case a given closed set ?, showed that is criterion ?-V-sufficient sufficient mappings. this paper discuss several equivalent or condition.