Books on functional equations

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.

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

Proving:$\tan(20^{\circ})\cdot \tan(30^{\circ}) \cdot \tan(40^{\circ})=\tan(10^{\circ})$

Spaces with the property: Uniformly continuous equals continuous

Two atlases on a manifold $M$ are equivalent if and only if they determine the same set of smooth functions $f:M\rightarrow\mathbb{R}$

If for any $k$, $\sum\limits_{n=0}^\infty a_n^k=\sum\limits_{n=0}^\infty b_n^k$, then$(a_n)=(b_{σ(n)}),\ σ \in{\mathfrak S}_{\mathbb N}$

Does $\frac{1}{n}\sum_{i=1}^n|x_i|\to L<\infty$ imply $\frac{1}{n}\max_{1\leq i\leq n}|x_i|=0$?

Showing groups of order $p^{k}(p+1)$ are not simple, p prime

Complex eigenvalues of a rotation matrix

Dirichlet series

Algorithms for finding the multiplicative order of an element in a group of integers mod m

Vector spaces: Is (the) scalar multiplication unique?

$12$ Identical balls can be placed into $3$ identical boxes,