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Miklós Schweitzer
1960 Miklós Schweitzer
3
3
Part of
1960 Miklós Schweitzer
Problems
(1)
Miklós Schweitzer 1960- Problem 3
Source:
11/18/2015
3. Let
f
(
z
)
f(z)
f
(
z
)
with
f
(
0
)
=
1
f(0)=1
f
(
0
)
=
1
be regular in the unit disk and let
[
∂
2
∣
f
(
z
)
∣
∂
x
∂
y
]
z
=
0
=
1
\left [\frac{\partial^2 \mid f(z)\mid}{\partial x\partial y} \right ] _{z=0} =1
[
∂
x
∂
y
∂
2
∣
f
(
z
)
∣
]
z
=
0
=
1
.Show thatthe area of the image of the unit disk by
w
=
f
(
z
)
w= f(z)
w
=
f
(
z
)
(taken with multiplicity) is not less than
1
2
\frac {1} {2}
2
1
.(f. 6)
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