MathDB

functional inequality

Source: Middle European Mathematical Olympiad T-2

September 21, 2014

inequalitiesfunctionalgebra proposedalgebra

Problem Statement

Determine all functions

f : \mathbb{R} \to \mathbb{R}

such that

xf(xy) + xyf(x) \ge f(x^2)f(y) + x^2y

holds for all

x,y \in \mathbb{R}