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2013 Benelux
2
Functional: f(x+y)+y<f^(3)(x)
Functional: f(x+y)+y<f^(3)(x)
Source: Benelux MO 2013 Q2
April 29, 2013
function
algebra
Functional inequality
Problem Statement
Find all functions
f
:
R
→
R
f: \mathbb{R} \to \mathbb{R}
f
:
R
→
R
such that
f
(
x
+
y
)
+
y
≤
f
(
f
(
f
(
x
)
)
)
f(x + y) + y \le f(f(f(x)))
f
(
x
+
y
)
+
y
≤
f
(
f
(
f
(
x
)))
holds for all
x
,
y
∈
R
x, y \in \mathbb{R}
x
,
y
∈
R
.
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