Where can I find a proof of the following fact?

>If
$$w(u,x_{0},r)=\sup _{B_{r}(x_{0})}u-\inf _{B_{r}(x_{0})}u$$
for some function $u(x)$ satisfies
$$ w\left(u,x_{0},{\tfrac {r}{2}}\right)\leq \lambda w\left(u,x_{0},r\right)$$
for a fixed $0 < \lambda < 1$ and all sufficiently small values of $r$, then $u$ is Hölder continuous.