New posts in functional-equations

$f(a+b)=f(a)+f(b)$ but $f$ is not linear

real-analysis linear-algebra abstract-algebra functional-equations

Additivity + Measurability $\implies$ Continuity

measure-theory continuity functional-equations

Is there a bijective seacucumber?

real-analysis continuity examples-counterexamples functional-equations

BMO1 2009/10 Q5 functional equation: $f(x)f(y) = f(x + y) + xy$

functions contest-math functional-equations

Recreational math: If $f(f(x))=e^x$, bound the integral $\int_0^1 f(x)dx$

integration definite-integrals recreational-mathematics functional-equations upper-lower-bounds

Prove that this function is bounded

real-analysis functional-equations asymptotics

How to find $f$ if $f(f(x))=\frac{x+1}{x+2}$

functional-equations

How prove there is no continuous functions $f:[0,1]\to \mathbb R$, such that $f(x)+f(x^2)=x$.

calculus analysis continuity power-series functional-equations

How to calculate $f(x)$ in $f(f(x)) = e^x$?

power-series functional-equations tetration

If $f\colon \mathbb{R} \to \mathbb{R}$ is such that $f (x + y) = f (x) f (y)$ and continuous at $0$, then continuous everywhere

real-analysis analysis functional-equations

Show that $f(x+y)=f(x)+f(y)$ implies $f$ continuous $\Leftrightarrow$ $f$ measurable [duplicate]

real-analysis functional-equations

Finding all $ f : \mathbb R \to \mathbb R $ satisfying $ f \bigl ( f ( x ) f ( y ) \bigr ) + f ( x + y ) = f ( x y ) $ for all $ x , y \in \mathbb R $

contest-math functional-equations

$f(a)+f(-b)=0$ implies $f(-a)+f(b)=0$. Then $f$ is an odd function?

real-analysis functions functional-equations even-and-odd-functions

Do there exist functions satisfying $f(x+y)=f(x)+f(y)$ that aren't linear?

functional-equations

About finding the function such that $f(xy)=f(x)f(y)-f(x+y)+1$ [duplicate]

functions functional-equations

Find all functions $f(x)$ such that $f\left(x^2+f(y)\right)$=$y+(f(x))^2$

functional-equations

On sort-of-linear functions: does $f(x+y) = f(x) + f(y)$ imply $f(\alpha x) = \alpha f(x)$?

functions functional-equations

Find all polynomials $P$ such that $P(x^2+1)=P(x)^2+1$

polynomials functional-equations contest-math

Is it true that this function $f(n)=n^{13}$?

functions contest-math functional-equations

Examples of functions where $f(ab)=f(a)+f(b)$

functional-equations