  We present the results from a survey of 57 low-redshift Abell galaxy clusters
to study the radial dependence of the luminosity function (LF). The dynamical
radius of each cluster, r200, was estimated from the photometric measurement of
cluster richness, Bgc. The shape of the LFs are found to correlate with radius
such that the faint-end slope, alpha, is generally steeper on the cluster
outskirts. The sum of two Schechter functions provides a more adequate fit to
the composite LFs than a single Schechter function. LFs based on the selection
of red and blue galaxies are bimodal in appearance. The red LFs are generally
flat for -22 < M_Rc < -18, with a radius-dependent steepening of alpha for M_Rc
> -18. The blue LFs contain a larger contribution from faint galaxies than the
red LFs. The blue LFs have a rising faint-end component (alpha ~ -1.7) for M_Rc
> -21, with a weaker dependence on radius than the red LFs. The dispersion of
M* was determined to be 0.31 mag, which is comparable to the median measurement
uncertainty of 0.38 mag. This suggests that the bright-end of the LF is
universal in shape at the 0.3 mag level. We find that M* is not correlated with
cluster richness when using a common dynamical radius. Also, we find that M* is
weakly correlated with BM-type such that later BM-type clusters have a brighter
M*. A correlation between M* and radius was found for the red and blue galaxies
such that M* fades towards the cluster center.
