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Erdős problem 1125

Let f:RRf:\mathbb{R}\to \mathbb{R} be such that 2f(x)f(x+h)+f(x+2h)2f(x) \leq f(x+h)+f(x+2h) for every xRx\in \mathbb{R} and h>0h>0. Must ff be monotonic?

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