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National and Regional Contests
Switzerland Contests
Switzerland - Final Round
2008 Switzerland - Final Round
2
2
Part of
2008 Switzerland - Final Round
Problems
(1)
f(xy) <= 1/2 (xf(y) + yf(x) )
Source: Switzerland - 2008 Swiss MO Final Round p2
12/26/2022
Determine all functions
f
:
R
+
→
R
+
f : R^+ \to R^+
f
:
R
+
→
R
+
, so that for all
x
,
y
>
0
x, y > 0
x
,
y
>
0
:
f
(
x
y
)
≤
x
f
(
y
)
+
y
f
(
x
)
2
f(xy) \le \frac{xf(y) + yf(x)}{2}
f
(
x
y
)
≤
2
x
f
(
y
)
+
y
f
(
x
)
algebra
inequalities
Functional inequality
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