  The inclusive gluon production at midrapidities is described in the Color
Glass Condensate formalism using the $k_T$ - factorization formula, which was
derived at fixed coupling constant considering the scattering of a dilute
system of partons with a dense one. Recent analysis demonstrated that this
approach provides a satisfactory description of the experimental data for the
inclusive hadron production in $pp/pA/AA$ collisions. However, these studies
are based on the fixed coupling $k_T$ - factorization formula, which does not
take into account the running coupling corrections, which are important to set
the scales present in the cross section. In this paper we consider the running
coupling corrected $k_T$ - factorization formula conjectured some years ago and
investigate the impact of the running coupling corrections on the observables.
In particular, the pseudorapidity distributions and charged hadrons
multiplicity are calculated considering $pp$, $dAu/pPb$ and $AuAu/PbPb$
collisions at RHIC and LHC energies. We compare the corrected running coupling
predictions with those obtained using the original $k_T$ - factorization
assuming a fixed coupling or a prescription for the inclusion of the running of
the coupling. Considering the Kharzeev - Levin - Nardi unintegrated gluon
distribution and a simplified model for the nuclear geometry, we demonstrate
that the distinct predictions are similar for the pseudorapidity distributions
in $pp/pA/AA$ collisions and for the charged hadrons multiplicity in $pp/pA$
collisions. On the other hand, the running coupling corrected $k_T$ -
factorization formula predicts a smoother energy dependence for $dN/d\eta$ in
$AA$ collisions.
