  We study the galaxy cosmological mass function (GCMF) in a semi-empirical
relativistic approach using observational data provided by galaxy redshift
surveys. Starting from the theory of Ribeiro & Stoeger (2003,
arXiv:astro-ph/0304094) between the mass-to-light ratio, the selection function
obtained from the luminosity function (LF) data and the luminosity density, the
average luminosity $L$ and the average galactic mass $\mathcal{M}_g$ are
computed in terms of the redshift. $\mathcal{M}_g$ is also alternatively
estimated by a method that uses the galaxy stellar mass function (GSMF).
Comparison of these two forms of deriving the average galactic mass allows us
to infer a possible bias introduced by the selection criteria of the survey. We
used the FORS Deep Field galaxy survey sample of 5558 galaxies in the redshift
range $0.5 < z < 5.0$ and its LF Schechter parameters in the B-band, as well as
this sample's stellar mass-to-light ratio and its GSMF data. Assuming
${\mathcal{M}_{g_0}} \approx 10^{11} \mathcal{M}_\odot$ as the local value of
the average galactic mass, the LF approach results in $L_{B} \propto
(1+z)^{(2.40 \pm 0.03)}$ and $\mathcal{M}_g \propto (1+z)^{(1.1\pm0.2)}$.
However, using the GSMF results produces $\mathcal{M}_g \propto (1+z)^{(-0.58
\pm 0.22)}$. We chose the latter result as it is less biased. We then obtained
the theoretical quantities of interest, such as the differential number counts,
to calculate the GCMF, which can be fitted by a Schechter function. The derived
GCMF follows theoretical predictions in which the less massive objects form
first, being followed later by more massive ones. In the range $0.5 < z < 2.0$
the GCMF has a strong variation that can be interpreted as a higher rate of
galaxy mergers or as a strong evolution in the star formation history of these
galaxies.
