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Miklós Schweitzer 1958- Problem 8

Source:

October 23, 2015

functioncollege contestsMiklos Schweitzer

Problem Statement

8. Let the function

f(x)

be periodic with the period

1

, non-negative, concave in the interval

(0,1)

and continuous at the point

0

. Prove that

f(nx)\leq nf(x)

for every real

x

and positive integer

n

. (R. 6)

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