  We study the connection between the observed star formation rate-stellar mass
(SFR-$M_*$) relation and the evolution of the stellar mass function (SMF) by
means of a Subhalo Abundance Matching technique coupled to merger trees
extracted from a N-body simulation. Our approach, which considers both galaxy
mergers and stellar stripping, is to force the model to match the observed SMF
at redshift $z>2$, and let it evolve down to the present time according to the
observed (SFR-$M_*$) relation. In this study, we use two different sets of SMFs
and two SFR-$M_*$ relations: a simple power law and a relation with a
mass-dependent slope. Our analysis shows that the evolution of the SMF is more
consistent with a SFR-$M_*$ relation with a mass-dependent slope, in agreement
with predictions from other models of galaxy evolution and recent observations.
In order to fully and realistically describe the evolution of the SMF, both
mergers and stellar stripping must be considered, and we find that both have
almost equal effects on the evolution of SMF at the massive end. Taking into
account the systematic uncertainties in the observed data, the high-mass end of
the SMF obtained by considering stellar stripping results in good agreement
with recent observational data from the Sloan Digital Sky Survey (SDSS). At
$\log M_* < 11.2$, our prediction at z=0.1 is close to \citet{li-white09} data,
but the high-mass end ($\log M_* > 11.2$) is in better agreement with
\citet{dsouza15} data which account for more massive galaxies.
