MathDB
Problems
Contests
Undergraduate contests
Miklós Schweitzer
1958 Miklós Schweitzer
8
8
Part of
1958 Miklós Schweitzer
Problems
(1)
Miklós Schweitzer 1958- Problem 8
Source:
10/23/2015
8. Let the function
f
(
x
)
f(x)
f
(
x
)
be periodic with the period
1
1
1
, non-negative, concave in the interval
(
0
,
1
)
(0,1)
(
0
,
1
)
and continuous at the point
0
0
0
. Prove that
f
(
n
x
)
≤
n
f
(
x
)
f(nx)\leq nf(x)
f
(
n
x
)
≤
n
f
(
x
)
for every real
x
x
x
and positive integer
n
n
n
. (R. 6)
function
college contests
Miklos Schweitzer