MathDB
No function satisfies inequality

Source: Romanian TST 2001

January 16, 2011
functioninequalitiesalgebra unsolvedalgebra

Problem Statement

Prove that there is no function f:(0,)(0,)f:(0,\infty )\rightarrow (0,\infty) such that f(x+y)f(x)+yf(f(x))f(x+y)\ge f(x)+yf(f(x)) for every x,y(0,)x,y\in (0,\infty ).