The Smoothness of Fractal Interpolation Functions on ℝ and on 𝑝-Series Local Fields

Figure 1

The graph of 𝑔(𝑥) in Example 7 with 𝜆=0.5 and the graph of the corresponding Weierstrass function 𝑊_𝜆(𝑥) with 𝜆=0.5.

(a)

(b)