MathDB
f(xf(y))+f(yf(z))+f(zf(x))=xy+yz+zx , in R_+

Source: 2020 Greek TST p1

November 14, 2020
algebrafunctionalfunctional equation

Problem Statement

Let R+=(0,+∞)R_+=(0,+\infty). Find all functions f:R+→R+f: R_+ \to R_+ such that
f(xf(y))+f(yf(z))+f(zf(x))=xy+yz+zxf(xf(y))+f(yf(z))+f(zf(x))=xy+yz+zx, for all x,y,z∈R+x,y,z \in R_+.
by Athanasios Kontogeorgis (aka socrates)
Back to ProblemsView on AoPS