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 $dN/deta$ in $AA$ collisions.
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