  In this paper, we investigate the differential cross sections of the
inclusive jet and dijet productions of the ZEUS collaboration data at the
center of mass energies of $\sim 300\;GeV$ and $ 319\;GeV$ using the $k_t$ and
$(z,k_t)\textrm{-factorizations}$ with the different unintegrated and double
unintegrated parton distribution functions, i.e., UPDFs and DUPDFs,
respectively. The \textsc{KaTie} event generator is used to calculate the
differential cross section with the UPDFs, while for the input DUPDFs the
calculations are directly performed by evaluating the corresponding matrix
elements. We check the effect of choosing the different implementation of
angular or strong ordering constraints using the UPDFs and the corresponding
DUPDFs of Kimber-Martin-Ryskin (KMR) and the leading-order (LO) and
next-to-leading-order (NLO) Martin-Ryskin-Watt (MRW) approaches. The impacts of
choosing virtualities $k^2 = k_t^2$ or $k^2 = {k_t^2\over {(1-z)}}$ in the
differential cross section predictions for the ZEUS experimental data are also
investigated. It is observed that, as one should expect, the applications of
$(z,k_t)\textrm{-factorization}$ is better than the
$k_t\textrm{-factorization}$ framework for the predictions of high virtuality
$Q^2$ with respect to the ZEUS collaboration data, and also the results of the
KMR and LO-MRW UPDFs and DUPDFs are reasonably close to each other and in
general can describe the data. It is also observed that only in the case of
$k_t$-factorization, the inclusion of Born level makes our results to overshoot
the inclusive jet experimental data.
