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A three-variable functional inequality on non-negative reals

Source: Dutch TST 2024, 1.2

June 28, 2024

inequalitiesfunctionfunctional equationalgebra proposedalgebraFunctional inequality

Problem Statement

Find all functions

f:\mathbb{R}_{\ge 0} \to \mathbb{R}

with

2x^3zf(z)+yf(y) \ge 3yz^2f(x)

for all

x,y,z \in \mathbb{R}_{\ge 0}