  A comparison between published field galaxy stellar mass functions (GSMFs)
shows that the cosmic stellar mass density is in the range 4--8 per cent of the
baryon density (assuming Omega_b = 0.045). There remain significant sources of
uncertainty for the dust correction and underlying stellar mass-to-light ratio
even assuming a reasonable universal stellar initial mass function. We
determine the z < 0.05 GSMF using the New York University - Value-Added Galaxy
Catalog sample of 49968 galaxies derived from the Sloan Digital Sky Survey and
various estimates of stellar mass. The GSMF shows clear evidence for a low-mass
upturn and is fitted with a double Schechter function that has alpha_2 =~ -1.6.
At masses below ~ 10^8.5 Msun, the GSMF may be significantly incomplete because
of missing low surface-brightness galaxies. One interpretation of the stellar
mass-metallicity relation is that it is primarily caused by a lower fraction of
available baryons converted to stars in low-mass galaxies. Using this
principal, we determine a simple relationship between baryonic mass and stellar
mass and present an `implied baryonic mass function'. This function has a
faint-end slope, alpha_2 =~ -1.9. Thus, we find evidence that the slope of the
low-mass end of the galaxy mass function could plausibly be as steep as the
halo mass function. We illustrate the relationship between halo baryonic mass
function --> galaxy baryonic mass function --> GSMF. This demonstrates the
requirement for peak galaxy formation efficiency at baryonic masses ~ 10^11
Msun corresponding to a minimum in feedback effects. The baryonic-infall
efficiency may have levelled off at lower masses.
