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MathLinks Contest 2nd
3.1
0231 functional inequality 2nd edition Round 3 p1
0231 functional inequality 2nd edition Round 3 p1
Source:
May 10, 2021
inequalities
2nd edition
algebra
functional
Problem Statement
Determine all values of
a
∈
R
a \in R
a
∈
R
such that there exists a function
f
:
[
0
,
1
]
→
R
f : [0, 1] \to R
f
:
[
0
,
1
]
→
R
fulfilling the following inequality for all
x
≠
y
x \ne y
x
=
y
:
∣
f
(
x
)
−
f
(
y
)
∣
≥
a
.
|f(x) - f(y)| \ge a.
∣
f
(
x
)
−
f
(
y
)
∣
≥
a
.
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