Recurrence relation

hi,
i have the following recurrence relation:

$a(x)_{n+1} = a(x)_{n} f(y_{n+1})$

where f is a known function.
in the most general case the x's are of a continuous domain and we know nothing about the y_n 's.
in the most simple case, the x's are of a discrete bounded domain, and the y_n 's are a subgroup of the x's.

I want to assume as less as possible (i.e- be closest to the general case as possible), in order to solve this relation.
What are the needed assumptions, and how do i solve for them?
(im not looking for a specific answer. any reasonable solution will do)

thank you