MathDB

Hard functional inequality

Source: Bulgaria IMO/Balkan MO 1998 TST and EGMO TST 2016, Day 2, Problem 3

February 3, 2023

functioninequalities

Problem Statement

Prove that there is no function

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

such that

f(x)^2 \geq f(x+y)(f(x)+y)

for all

x,y \in \mathbb{R}^{+}