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I am not a mathematician, so what I ask might be trivial, however I couldn't find something relevant in the web. My question is the following:

Is there a formal notation for functions that comply the following

$$f(x_1, ..., x_n) = g(f(x_1), ..., g(f(x_n))$$

and if there is such a property, how is it called? The current, intuitive name I can think of is decomposable functions, but I don't know if formally there is such a thing.

Example 1: An additive function would be decomposable.

Example 2: A multiplicative function would also be decomposable

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2 Answers 2

I don't know of any standard terminology for this property. I think "decomposability" is a fine term when defined in context. An interesting example of such a function is $f(f(x)) = x^2+1$.

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I think the notion of homomorphism in universal algebra might be what you are looking for.

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