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Miklós Schweitzer
1957 Miklós Schweitzer
5
5
Part of
1957 Miklós Schweitzer
Problems
(1)
Miklós Schweitzer 1957- Problem 5
Source:
10/16/2015
5. Find the continuous solutions of the functional equation
f
(
x
y
z
)
=
f
(
x
)
+
f
(
y
)
+
f
(
z
)
f(xyz)= f(x)+f(y)+f(z)
f
(
x
yz
)
=
f
(
x
)
+
f
(
y
)
+
f
(
z
)
in the following cases:(a)
x
,
y
,
z
x,y,z
x
,
y
,
z
are arbitrary non-zero real numbers; (b)
a
<
x
,
y
,
z
<
b
(
1
<
a
3
<
b
)
a<x,y,z<b (1<a^{3}<b)
a
<
x
,
y
,
z
<
b
(
1
<
a
3
<
b
)
. (R. 13)
functional equation
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