Identifying a flex ribbon connector
They're "board to board" connectors, but are sometimes used on FPC as well - especially for things like TFT.

I am not sure of that specific model, but I use a similar one from Hirose (DF30FC-20DS-0.4V(82)).


It's not quite identical, but it should give you a starting point. 

This is one used on the Picadillo-35T board which looks a closer match:



Unfortunately I don't have a model number for that, though with a bit of pestering I may be able to find out.