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National and Regional Contests
Moldova Contests
Chisinau City MO
1976 Chisinau City MO
130
130
Part of
1976 Chisinau City MO
Problems
(1)
Chisinau MO p130 1976 X |f (x) - f (y) | <= | x - y|^a , a>1. constant
Source:
3/16/2021
Prove that the function
f
(
x
)
f (x)
f
(
x
)
satisfying the relation
∣
f
(
x
)
−
f
(
y
)
∣
≤
∣
x
−
y
∣
a
|f (x) - f (y) | \le | x - y|^a
∣
f
(
x
)
−
f
(
y
)
∣
≤
∣
x
−
y
∣
a
for any real numbers
x
,
y
x, y
x
,
y
and some number
a
>
1
a> 1
a
>
1
is constant.
algebra
function
functional