The italic style of the theorem paragraph should not be applied to the math tag.

Theorem. Let f:Δ⟶Δ,f : \Delta \longrightarrow \Delta, where Δ={z∈ℂ:|z|<1}\Delta=\{z\in\mathbb{C}: \vert z \vert \lt 1\}, be analytic with a∈Δa \in \Delta. Then

|f(z)−f(a)1−f(a)¯f(z)|≤|z−a1−a¯z| \left\vert\frac{f(z)-f(a)}{1-\overline{f(a)}f(z)}\right\vert\le \left\vert\frac{z-a}{1-\overline{a}z}\right\vert

for all |z|≤1\vert z \vert \le 1 and

|f′(a)|1−|f(a)| 2≤11−|a| 2. \frac{\vert f'(a)\vert}{1-\vert f(a)\vert^2}\le \frac{1}{1-\vert a \vert^2}.

Furthermore, equality holds iff ff realizes a conformal mapping of Δ\Delta onto itself.