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Could you help me please with some functional equations? I need some online books with exercises and some explanations. I'm interested in the Cauchy functional equation and Jensen functional equation.

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You can find recent results of functional equations in the following references.

  1. Marek Kuczma, An Introduction to the Theory of Functional Equations and Inequalities (Cauchy’s Equation and Jensen’s Inequality) Second Edition, ISBN 978-3-7643-8748-8 Birkhäuser Verlag

  2. P. Kannappan, Functional equations and inequalities with applications, ISBN 978-0-387-89491-1 Springer

  3. Stefan Czerwik, Functional Equations and Inequalities in Several Variables, World Scientific, ISBN 981-02-4837-7

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I know it is a bit late now but it is good for anyone looking it up:

I think the best introduction book to functional equations would be Engel's problem solving strategies. It is very easy for beginners to start with and would recommend it for anyone looking forward to studying this topic.

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Nice are the handouts by Evan Chen, "Introduction to Functional Equations" and "Monsters".

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I think mathlink is the best one. Usually, books about functional equations include old problems only(some of them doesn't even include problems made in 21th century...) But if you search 'functional equation' on Forum(which is in the 'Community' section), there are a lot of challenging problems, and you might see tons of amazing techniques in FE!!!

Here's the link : https://artofproblemsolving.com/

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  • $\begingroup$ Additionally, techniques in functional equations are not 'theoretical'. I usually learned techniques by solving hard problems, and there are problems that require high-level technique. $\endgroup$ Commented Apr 23, 2020 at 16:30

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