When it comes to asking for all solutions, it may be the case that conditions from mathematical analysis should be applied; for example, in the case of the Cauchy equation mentioned above, the solutions that are continuous functions are the 'reasonable' ones, while other solutions that are not likely to have practical application can be constructed (by using a Hamel basis for the real numbers as vector space over the rational numbers).
[citation needed] Some solutions to functional equations have exploited surjectivity, injectivity, oddness, and evenness.
[citation needed] Some functional equations have been solved with the use of ansatzes, mathematical induction.
[citation needed] Some classes of functional equations can be solved by computer-assisted techniques.
[vague][4] In dynamic programming a variety of successive approximation methods[5][6] are used to solve Bellman's functional equation, including methods based on fixed point iterations.