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International Zhautykov Olympiad
2016 International Zhautykov Olympiad
1
Functional inequality
Functional inequality
Source: IZHO2016
January 16, 2016
inequalities
Problem Statement
Find all
k
>
0
k>0
k
>
0
for which a strictly decreasing function
g
:
(
0
;
+
∞
)
→
(
0
;
+
∞
)
g:(0;+\infty)\to(0;+\infty)
g
:
(
0
;
+
∞
)
→
(
0
;
+
∞
)
exists such that
g
(
x
)
≥
k
g
(
x
+
g
(
x
)
)
g(x)\geq kg(x+g(x))
g
(
x
)
≥
k
g
(
x
+
g
(
x
))
for all positive
x
x
x
.
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