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Functional equation
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==Solution== One method of solving elementary functional equations is substitution.{{citation needed|date=March 2022}} Some solutions to functional equations have exploited [[surjective|surjectivity]], [[injective function|injectivity]], [[odd function|oddness]], and [[even function|evenness]].{{citation needed|date=March 2022}} Some functional equations have been solved with the use of [[ansatz]]es, [[mathematical induction]].{{citation needed|date=March 2022}} Some classes of functional equations can be solved by computer-assisted techniques.{{vague|reason="Computer assisted" is far too vague. What kinds of techniques were these?|date=March 2022}}<ref>{{Cite journal|last=HΓ‘zy|first=Attila| date=2004-03-01| title=Solving linear two variable functional equations with computer|journal=Aequationes Mathematicae| language=en| volume=67|issue=1|pages=47β62|doi=10.1007/s00010-003-2703-9|s2cid=118563768|issn=1420-8903}}</ref> In [[dynamic programming]] a variety of successive approximation methods<ref>Bellman, R. (1957). Dynamic Programming, [[Princeton University Press]].</ref><ref>Sniedovich, M. (2010). Dynamic Programming: Foundations and Principles, [[Taylor & Francis]].</ref> are used to solve [[Bellman equation|Bellman's functional equation]], including methods based on [[fixed point iteration]]s.
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