Functional Equation for Non negative Reals
Source: 2009 Japan Mathematical Olympiad Finals, Problem 5
February 21, 2009
functioninequalitiessymmetryalgebra proposedalgebra
Problem Statement
Find all functions , defined on the non negative real numbers and taking non negative real numbers such that f(x^2)\plus{}f(y)\equal{}f(x^2\plus{}y\plus{}xf(4y)) for any non negative real numbers .