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.
You can find recent results of functional equations in the following references.
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
P. Kannappan, Functional equations and inequalities with applications, ISBN 978-0-387-89491-1 Springer
Stefan Czerwik, Functional Equations and Inequalities in Several Variables, World Scientific, ISBN 981-02-4837-7
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.