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replaced http://mathoverflow.net/ with https://mathoverflow.net/

About literature related to the topic of this question:

In the answer to the question f(f(x))=exp(x)-1 and other functions “just in the middle” between linear and exponential. one can find an interesting link with many references related to the problem:

There is also Kindermanns PhD thesis about finding solutions to iterative functional equations using a neural network (in german only)

which might be helpful.

user4503
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