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f(xy) <= 1/2 (xf(y) + yf(x) )

Source: Switzerland - 2008 Swiss MO Final Round p2

December 26, 2022
algebrainequalitiesFunctional inequalityfunctional

Problem Statement

Determine all functions f:R+→R+f : R^+ \to R^+, so that for all x,y>0x, y > 0: f(xy)≤xf(y)+yf(x)2f(xy) \le \frac{xf(y) + yf(x)}{2}
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