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Complex Analysis
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Schwarz Lemma
Schwarz Lemma
📜
The statement of the theorem
If
f
f
f
is holomorphic in the unit disk,
f
(
0
)
=
0
f(0)=0
f
(
0
)
=
0
, and
∣
f
(
z
)
∣
≤
1
|f(z)| \le 1
∣
f
(
z
)
∣
≤
1
, then
∣
f
(
z
)
∣
≤
∣
z
∣
|f(z)| \le |z|
∣
f
(
z
)
∣
≤
∣
z
∣
and
∣
f
′
(
0
)
∣
≤
1
|f'(0)| \le 1
∣
f
′
(
0
)
∣
≤
1
.
Source: Wikipedia