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2023 ISL
A4
A4
Part of
2023 ISL
Problems
(1)
another functional inequality?
Source: 2023 ISL A4
7/17/2024
Let
R
>
0
\mathbb R_{>0}
R
>
0
be the set of positive real numbers. Determine all functions
f
:
R
>
0
→
R
>
0
f \colon \mathbb R_{>0} \to \mathbb R_{>0}
f
:
R
>
0
→
R
>
0
such that
x
(
f
(
x
)
+
f
(
y
)
)
⩾
(
f
(
f
(
x
)
)
+
y
)
f
(
y
)
x \left(f(x) + f(y)\right) \geqslant \left(f(f(x)) + y\right) f(y)
x
(
f
(
x
)
+
f
(
y
)
)
⩾
(
f
(
f
(
x
))
+
y
)
f
(
y
)
for every
x
,
y
∈
R
>
0
x, y \in \mathbb R_{>0}
x
,
y
∈
R
>
0
.
algebra
Functional inequality
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