Functional eqn....

Nice. f(x) = c for some real c≥0 is the only family of functions satisfying the given relation.

Proof: Putting y=z=0, we get 2 f(x) + f(0) ≥ 3 f(x) or f(0)≥f(x) for all x

Again putting x=y=-z, we get f(-2z)≥f(0) for all z in other words f(t)≥f(0) for all real t.

This means f(x) = f(0) for all real x i.e. f(x) is a constant