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Problems
Contests
National and Regional Contests
Netherlands Contests
Dutch BxMO/EGMO TST
2023 Dutch BxMO TST
2
2
Part of
2023 Dutch BxMO TST
Problems
(1)
Asymmetric functional inequality from the Netherworld
Source: 2023 Dutch BxMO TST, Problem 2
3/12/2024
Find all functions
f
:
R
→
R
f : \mathbb R \to \mathbb R
f
:
R
→
R
for which
f
(
a
−
b
)
f
(
c
−
d
)
+
f
(
a
−
d
)
f
(
b
−
c
)
≤
(
a
−
c
)
f
(
b
−
d
)
,
f(a - b) f(c - d) + f(a - d) f(b - c) \leq (a - c) f(b - d),
f
(
a
−
b
)
f
(
c
−
d
)
+
f
(
a
−
d
)
f
(
b
−
c
)
≤
(
a
−
c
)
f
(
b
−
d
)
,
for all real numbers
a
,
b
,
c
a, b, c
a
,
b
,
c
and
d
d
d
. Note that there is only one occurrence of
f
f
f
on the right hand side!
Functional Equations
Functional inequality
algebra