MathDB

2yf(x+y) + (x-y)(f(x) + f(y)) >= 0

Source: AIMO 2008, TST 5, P3, Suggested by Gunther Vogel

January 4, 2009

algebrapolynomialinequalitiesalgebra unsolved

Problem Statement

Find all real polynomials

f

with

x,y \in \mathbb{R}

such that 2 y f(x \plus{} y) \plus{} (x \minus{} y)(f(x) \plus{} f(y)) \geq 0.