We analyze the Luminosity Functions ( LFs ) of a subsample of 69 clusters from the RASS-SDSS galaxy cluster catalog .
When calculated within the cluster physical sizes , given by r _ { 200 } or r _ { 500 } , all the cluster LFs appear to have the same shape , well fitted by a composite of two Schechter functions with a marked upturn and a steepening at the faint-end .
Previously reported cluster-to-cluster variations of the LF faint-end slope are due to the use of a metric cluster aperture for computing the LF of clusters of different masses .

We determine the composite LF for early- and late-type galaxies , where the typing is based on the galaxy u - r colors .
The late-type LF is well fitted by a single Schechter function with a steep slope ( \alpha = -2.0 in the r band , within r _ { 200 } ) .
The early-type LF instead can not be fitted by a single Schechter function , and a composite of two Schechter functions is needed .
The faint-end upturn of the global cluster LF is due to the early-type cluster galaxies .
The shape of the bright-end tail of the early-type LF does not seem to depend upon the local galaxy density or the distance from the cluster center .
The late-type LF shows a significant variation only very near the cluster center .
On the other hand , the faint-end tail of the early-type LF shows a significant and continuous variation with the environment .

We provide evidence that the process responsible for creating the excess population of dwarf early type galaxies in clusters is a threshold process that occurs when the density exceeds \sim 500 times the critical density of the Universe .

We interpret our results in the context of the ’ harassment ’ scenario , where faint early-type cluster galaxies are predicted to be the descendants of tidally-stripped late-type galaxies .