I am dealing with $f:[0,T]\to\Bbb R$, $\;\alpha$-Hölder continuous functions, with $\frac12<\alpha\le1$ such that $f(0)=0$, nowhere differentiable.
Let us denote the space of such functions with $\mathcal C^{\alpha}[0,T]$.
I already know that every function in such space is approximated in Hölder norm (not only in sup-norm!) by its Bernstein polynomials.
However I was asking myself if something similar does hold for different kind of approximating functions, which can be written explicitly as well.