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Balkan MO Shortlist
2021 Balkan MO Shortlist
A2
BMO Shortlist 2021 A2
BMO Shortlist 2021 A2
Source: BMO Shortlist 2021
May 8, 2022
Balkan
shortlist
2021
algebra
Functional inequality
Problem Statement
Find all functions
f
:
R
→
R
f: \mathbb{R} \rightarrow \mathbb{R}
f
:
R
→
R
such that
f
(
x
2
+
y
)
≥
(
1
x
+
1
)
f
(
y
)
f(x^2 + y) \ge (\frac{1}{x} + 1)f(y)
f
(
x
2
+
y
)
≥
(
x
1
+
1
)
f
(
y
)
holds for all
x
∈
R
∖
{
0
}
x \in \mathbb{R} \setminus \{0\}
x
∈
R
∖
{
0
}
and all
y
∈
R
y \in \mathbb{R}
y
∈
R
.
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