If $f$ is a complex-valued function analytic on $\{z:\vert z \vert \leqq r \}$, then for $\vert z \vert
$ \vert f(z) \vert \leqq \frac{2\vert z \vert}{2-\vert z \vert} \sup\{\Re f(w): \vert w \vert=\vert z \vert\}+\frac{r+\vert z \vert}{r-\vert z \vert}\vert f(0) \vert. $