discontinuous solutions of the functional equation $f\left(a^b\right) = f(a)^{f(b)}$
32599
Solution to the functional equation $f(x^y)=f(x)^{f(y)}$
88683
Functional equation $f\left(\frac{x+y}{2}\right)+f\left(\frac{2xy}{x+y}\right)=f(x)+f(y)$ implies $2f(\sqrt{xy})=f(x)+f(y)$
136475
d'Alembert-like functional equation: $f(x+y)+g(x-y)=\lambda f(x)g(y)$
141223
$f(x^2) = 2f(x)$ and $f(x)$ continuous
34398
Prove $\left| \int_a^b f(t) dt \right| \leq \int_a^b \left| f(t) \right| dt$
62111
Functional Equation $f(mn)=f(m)f(n)$.
24810
Functions satisfying $(b-a)f'(\tfrac{a+b}{2}) = f(b)- f(a)$
62966
Find all functions $f(x)$ such that $f\left(x^2+f(y)\right)$=$y+(f(x))^2$
20688
Discontinuous functions with closed graphs
7358
For each $y \in \mathbb{R}$ either no $x$ with $f(x) = y$ or two such values of $x$. Show that $f$ is discontinuous.
150346
If $f$ is an increasing function defined on $[a,b]$ . Then, $f$ has countable number of discontinuities
76458
Solve the following functional equation $f(xf(y))+f(yf(x))=2xy$
132093
Solve $f(f(x))=f(x)$
15820
Discontinuous linear functional
76679
Prove there are no other solutions of functional equation $f(x+y) = \frac{f(x)+f(y)}{1-f(x)f(y)}$
38886
Discontinuous function on Q
13270
Prove $\exists \xi \in (a,b):f'(\xi)<1+f^2(\xi)$