The growth factor parametrization versus numerical solutions in flat and
  non-flat dark energy models
  In the present investigation we use observational data of $ f \sigma_ {8} $
to determine observational constraints in the plane $(\Omega_{m0},\sigma_{8})$
using two different methods: the growth factor parametrization and the
numerical solutions method for density contrast, $\delta_{m}$. We verified the
correspondence between both methods for three models of accelerated expansion:
the $\Lambda CDM$ model, the $ w_{0}w_{a} CDM$ model and the running
cosmological constant $RCC$ model. In all case we consider also curvature as
free parameter. The study of this correspondence is important because the
growth factor parametrization method is frequently used to discriminate between
competitive models. Our results we allow us to determine that there is a good
correspondence between the observational constrains using both methods. We also
test the power of the $ f\sigma_ {8} $ data to constraints the curvature
parameter within the $ \Lambda CDM $ model. For this we use a non-parametric
reconstruction using Gaussian processes. Our results show that the $ f\sigma_
{8}$ data with the current precision level does not allow to distinguish
between a flat and non-flat universe.
