MathDB
strange function

Source: brazilian selection test,2001

January 8, 2014
functionalgebra proposedalgebra

Problem Statement

Find all functions f f defined on real numbers and taking values in the set of real numbers such that f(x+y)+f(y+z)+f(z+x)≥f(x+2y+3z) f(x+y)+f(y+z)+f(z+x) \geq f(x+2y+3z) for all real numbers x,y,z x,y,z .
There is an infinity of such functions. Every function with the property that 3inf⁡f≥sup⁡f 3 \inf f \geq \sup f is a good one. I wonder if there is a way to find all the solutions. It seems very strange.
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