Let a, b be constants such that a lessthanorequalto I and b > I, let f(n) be a function and let T(n) be defined on natural numbers by the recurrence T (n) = a T (n/b) + f (n). Then T(n) can be bounded asymptotically as follows: 1) If f(n) = O (n^log b^a - epsilon) for some epsilon > 0, then T(n) = theta (n^log b^a) 2) If f(n) = theta (n^log b^a) then T(n) = theta (n^log b^a log n) 3) If f(n) = ohm (n^log b^a + epsilon) for some epsilon > 0, and if a f(n/b) lessthanorequalto c f(n) for some constant c