2012-13 functions for an inequality

Determine all nonnegative functions f(x,y) and g(x,y) such that $\left(\sum_{i=1}^n a_i b_i \right)^2 \le \left( \sum_{i=1}^n f(a_i,b_i)\right) \left(\sum_{i=1}^n g(a_i,b_i)\right) \le \left(\sum_{i=1}^n a_i^2\right) \left(\sum_{i=1}^n b_i^2\right)$ for all reals $$a_i$$, $$b_i$$ and all positive integers n.

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