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In this work, we discuss: (i) The ratios of different parton distributionfunctions (PDFs), i.e., MMHT2014, CJ15, CTEQ6l1, HERAPDF15, MSTW2008, HERAPDF20and MSHT20, and the corresponding Kimber-Martin-Ryskin (KMR) unintegratedparton distribution functions (UPDFs) sets versus the hard scale $Q^2$, to findout the sensibility of the KMR UPDFs with respect to the input PDFs sets. It isshown that there is not much difference between the different input-PDFs orcorresponding UPDFs sets ratios. (ii) Then, the dependence of proton$k_t$-factorization structure functions on the different UPDFs sets which canuse the above PDFs sets as input, are presented. The results are compared withthe experimental data of ZEUS, NMC and H1+ZEUS at the hard scale $Q^2 =27$ and$90$ $GeV^2$, and a reasonable agreement is found, considering different inputPDFs sets. (iii) Furthermore, by fitting a Gaussian function, which depends onthe transverse momentum $k_t$, to the KMR UPDFs and averaging over $x$ (thefractional parton momentum), we obtain the average transverse momentum,$<k_t^2>$, in the scale range $Q^2=2.4-1.44\times10^4$ $GeV^2$, which is inagreement with the other groups predictions, $0.25-0.44$ $GeV^2$ at $Q^2=2.4$$GeV^2$. (iv) Finally we explore the average transverse momentum for which, theresults of proton structure function with the KMR UPDFs and that of theGaussian $k_t$-dependent, are consistent to each other. Through the abovereport, at each step the parton branching (PB) UPDFs, i.e., the transversemomentum dependent PDFs (PB TMDPDFs) are considered for comparisons with thecorresponding KMR UPDFs output.

On validity of different PDFs sets using the proton $k_t$-factorization structure functions and the Gaussian $k_t$-dependence of KMR UPDFs