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IMC
1999 IMC
4
there exists none
there exists none
Source: IMC 1999 day 2 problem 4
November 19, 2005
function
inequalities
limit
real analysis
real analysis unsolved
Problem Statement
Prove that there's no function
f
:
R
+
→
R
+
f: \mathbb{R}^+\rightarrow\mathbb{R}^+
f
:
R
+
→
R
+
such that
f
(
x
)
2
≥
f
(
x
+
y
)
(
f
(
x
)
+
y
)
f(x)^2\ge f(x+y)\left(f(x)+y\right)
f
(
x
)
2
≥
f
(
x
+
y
)
(
f
(
x
)
+
y
)
for all
x
,
y
>
0
x,y>0
x
,
y
>
0
.
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