  We discuss the existence of inflationary solutions in a class of
renormalization group improved polynomial f(R) theories, which have been
studied recently in the context of the asymptotic safety scenario for quantum
gravity. These theories seem to possess a nontrivial ultraviolet fixed point,
where the dimensionful couplings scale according to their canonical
dimensionality. Assuming that the cutoff is proportional to the Hubble
parameter, we obtain modified Friedmann equations which admit both power law
and exponential solutions. We establish that for sufficiently high order
polynomial the solutions are reliable, in the sense that considering still
higher order polynomials is very unlikely to change the solution.
