There are similar questions:
Finding 'closest' function subject to constraints on derivatives
Define a function given some constraints
Find a function given its poles, residues, limit at infinity, and additional constraints
but maybe this is more general.
Can one find a function given first order logic type constraints on the domain and range values, and even some range values (but not polynomial interpolation with just set of mappings) for example, say our mystery function is:
f(x) = x^2 + 1
But all we have are a set of constraints like:
forall x, f(x) < f(x+1)
forall x, f(x) < 2 * f(x+1)
f(1) = 2
f(10) = 101
Is it possible to produce a function (or functions) that satisfies the given constraints through some mathematical process or computation? What area of math is this?