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From definition of $o$ and $\omega$

one states that $0 < c_1\cdot g(n) < f(n)$ for $n > n_0$ and some $c_1$ and another states that $0 < f(n) < c_2\cdot g(n)$ for $n > n_1$ and some $c_2$

It seems like there is no such function that satisfies condition. But i can't show this rigorously.

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    Every $f$ and $g$ such that $f(n)=g(n)$ for every $n$ fulfill the condition written **in your post**.2011-11-11
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    I have tagged it as computer-science + asymptotics, based on the previous tag and the "computer-sciency" "definitions"...2012-02-09

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