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Austrian-Polish
1994 Austrian-Polish Competition
8
8
Part of
1994 Austrian-Polish Competition
Problems
(1)
f(x,y) = af (x,z) + bf(y,z)
Source: Austrian - Polish 1994 APMC
5/3/2020
Given real numbers
a
,
b
a, b
a
,
b
, find all functions
f
:
R
→
R
f: R \to R
f
:
R
→
R
satisfying
f
(
x
,
y
)
=
a
f
(
x
,
z
)
+
b
f
(
y
,
z
)
f(x,y) = af (x,z) + bf(y,z)
f
(
x
,
y
)
=
a
f
(
x
,
z
)
+
b
f
(
y
,
z
)
for all
x
,
y
,
z
∈
R
x,y,z \in R
x
,
y
,
z
∈
R
.
functional equation
functional
algebra