I have just learned about the concept of a "functional equation". So far as I understand, a functional equation is an equation that implicitly defines a function.
I've found an example, the "Abel equation": $f(h(x))=h(x+1)$
Firstly: is this a functional equation that defines $f$ or does it define $h$?
Secondly, how would I solve this Abel equation?
Thirdly, what is the relation between functional analysis and functional equations?