[see also: overview]
For an extensive survey of ......, see ......
For a survey of what is known to date, see [G].
A survey of the research on $f_n(x,y)$ up to 2007 (most of it dealing with the case $n=1$) was given in .
The survey article  by Diestel contains a wealth of information about the Dunford--Pettis property.
We cannot survey this whole subject here.
Other situations in dynamics where the $p$-adic numbers come up are surveyed in [W].