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Miklós Schweitzer
1954 Miklós Schweitzer
4
4
Part of
1954 Miklós Schweitzer
Problems
(1)
Miklós Schweitzer 1954- Problem 4
Source:
9/29/2015
4. Find all functions of two variables defined over the entire plane that satisfy the relations
f
(
x
+
u
,
y
+
u
)
=
f
(
x
,
y
)
+
u
f(x+u,y+u)=f(x,y)+u
f
(
x
+
u
,
y
+
u
)
=
f
(
x
,
y
)
+
u
and
f
(
x
v
,
y
v
)
=
f
(
x
,
y
)
v
f(xv,yv)= f(x,y) v
f
(
xv
,
y
v
)
=
f
(
x
,
y
)
v
for any real numbers
x
,
y
,
u
,
v
x,y,u,v
x
,
y
,
u
,
v
. (R.12)
function
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