MathDB

AM-GM functional inequality 2020

Source: IMOC 2020 A1

September 5, 2020

inequalitiesAM-GMalgebrafunctional equationIMOC

Problem Statement

\definecolor{A}{RGB}{190,0,60}\color{A}\fbox{A1.} Find all

f:\mathbb{R}\rightarrow \mathbb{R}

such that \definecolor{A}{RGB}{80,0,200}\color{A} x^4+y^4+z^4\ge f(xy)+f(yz)+f(zx)\ge xyz(x+y+z)holds for all

a,b,c\in\mathbb{R}

.
Proposed by [color=#FFFF00]usjl. [color=#B6D7A8]#1733