The Weierstrass function https://en.wikipedia.org/wiki/Weierstrass_function
is a pathological example of a continuous nowhere differentiable function.. Since a conttaction mapping is necessarily Lipschitz continuous (which is a stronger form of continuity), I was wondering if there exists a (pathological) example of a contraction mapping that is nowhere differentiable
Best Answer
No, by Rademacher's theorem a Lipschitz function $\Bbb R^n\to\Bbb R^n$ is differentiable almost everywhere. A proof of this result can be found, for example, in Emmanuele DiBenedetto's Real Analysis, Theorem 21.1.