  Jet production at hadron colliders provides constraints on the parton
distribution functions (PDFs) of the proton, in particular on the gluon
distribution. In the present paper, the impact on PDF of CMS inclusive
differential jet cross sections at center-of-mass energy of $\sqrt s = 8$ TeV
for jets with low momentum $p\mathrm{_T}$ and produced in the forward direction
is investigated at next-to leading order in perturbative quantum chromodynamics
(QCD). The results of the QCD global analysis are compared with theoretical
predictions. The impact of low-$p\mathrm{_T}$ jet measurements on the
determination of the gluon distribution is assessed. The inclusion of the
discussed measurements adds further constraints on the uncertainty of the gluon
distribution at large Bjorken $x > 0.1$, where the low-$p_T$ data have the
largest impact.
