Multiplication of non-convex functions is also non-convex?

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Consider that we have a set of non-convex functions $f_1, f_2, ...., f_n$. Is it also non-convex the multiplication of these functions? In other word, $f=f_1 \times f_2 \times...\times f_n$ is non-convex? Have anyone a reference article or book for this?

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For a counterexample, let $f_1(x)=f_2(x)=\sqrt x$.

See this answer: Proving that multiplication of convex function is convex