$1992$ IMO Functional Equation problem
62966
Find all functions $f(x)$ such that $f\left(x^2+f(y)\right)$=$y+(f(x))^2$
82280
Problem about continuous functions and the intermediate value theorem
136475
d'Alembert-like functional equation: $f(x+y)+g(x-y)=\lambda f(x)g(y)$
145339
Index of the subgroup $\operatorname{Im}(f)$
119270
Finding equation using hyperbolic transcendental functions.
62111
Functional Equation $f(mn)=f(m)f(n)$.
157744
Cauchy's functional equation with composite function: $gf(x+y)=gf(x)+gf(y)$
88683
Functional equation $f\left(\frac{x+y}{2}\right)+f\left(\frac{2xy}{x+y}\right)=f(x)+f(y)$ implies $2f(\sqrt{xy})=f(x)+f(y)$
13086
Overview of basic facts about Cauchy functional equation
129381
Modular equation problem
67249
Can you determine a formula for this problem?
11806
Functional equation.
100319
Functional equation with strange property about irrational numbers
26212
The $1997$ IIT JEE problem
71049
Functional equation $f(xy)=f(x)+f(y)$ and continuity
97994
Orthogonality Relations Exercise, Brezis' Book Functional Analysis
17175
Problem in solving functional equation $f(x^2 + yf(x)) = xf(x+y)$