Find all functions $f : (0, +\infty) \to (0, +\infty)$ which are increasing on $[1, +\infty)$ and for all positive reals $a, b, c$ they fulfill the following relation $f(ab)f(bc)f(ca)=f(a^2b^2c^2)+f(a^2)+f(b^2)+f(c^2)$.
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Tags: functional, algebra, 3rd edition
Find all functions $f : (0, +\infty) \to (0, +\infty)$ which are increasing on $[1, +\infty)$ and for all positive reals $a, b, c$ they fulfill the following relation $f(ab)f(bc)f(ca)=f(a^2b^2c^2)+f(a^2)+f(b^2)+f(c^2)$.