  We derived the conditions on certain combinations of integrals of the
fragmentation functions of pion using HERMES data of the sum for the charged
pion multiplicities from semi-inclusive deep-inelastic scattering (SIDIS) off
the deuteron target. In our derivation the nucleon parton distribution
functions (PDFs) are assumed to be isospin SU(2) symmetric. Similar conditions
have also been obtained for the fragmentation functions (FFs) of kaon by the
sum of charged kaon multiplicities as well. We have chosen several FFs to study
the impact of those conditions we have derived. Among those FFs, only that
produced in the nonlocal chiral-quark model (NL$\chi$QM) constantly satisfy the
conditions. Furthermore, the ratios of the strange PDFs $S(x)$ and the
nonstrange PDFs $Q(x,Q^2)$ extracted from the charged pion and kaon
multiplicities differ from each other significantly. Finally, we demonstrate
that the HERMES pion multiplicity data is unlikely to be compatible with the
two widely-used PDFs, namely CTEQ6M and NNPDF3.0.
