Bounds for Akra-Bazzi versus Master theorem
Both methods give $\Theta$ type estimates. That is, the master theorem gives some estimate $T = \Theta(f)$, and the Akra&ndash;Bazzi theorem gives some estimate $T = \Theta(g)$. From the definition of $\Theta$ it immediately follows that $f = \Theta(g)$ and $g = \Theta(f)$, that is, the estimates are equivalent. I suspect either one of you was mistaken, or both bounds that you got, while seemingly different, are in fact equivalent.