New posts in functional-equations

Find all functions f such that $f(f(x))=f(x)+x$

real-analysis functions functional-equations

Solving the Functional Equation $ f \big( x + y f ( x ) \big) = f ( x ) f ( y ) $

functional-equations

If $f(x+1)+f(x-1)=\sqrt 3 f(x), \forall x$ then $f$ is periodic.

functional-equations periodic-functions

Books on functional equations

reference-request functional-equations

How to prove $f(x)=ax$ if $f(x+y)=f(x)+f(y)$ and $f$ is locally integrable

calculus functional-equations

Can a conformal map be turned into an isometry?

differential-geometry riemannian-geometry functional-equations conformal-geometry

Solving $(f(x))^2 = f(\sqrt{2}x)$

calculus real-analysis functional-equations

Determining all the functions $f:\mathbb{R}\to\mathbb{R}$ with the property $f\bigl(x-f(y)\bigr) f\bigl(f(x)+y\bigr)=x f(x) - y f(y)$ [closed]

functions functional-equations

Different methods to prove $\zeta(s)=2^s\pi^{s-1}\sin\left(\frac{s\pi}{2}\right) \Gamma (1-s) \zeta (1-s)$.

complex-analysis special-functions functional-equations big-list riemann-zeta

Entire functions such that $f(z^{2})=f(z)^{2}$

complex-analysis functional-equations

Solve $f(x+f(2y))=f(x)+f(y)+y$

real-analysis functions functional-equations real-numbers

Find all $f$ which satisfies $ f:\mathbb{R}_{\geq0} \rightarrow \mathbb{R}, f(x+y^2) \geq f(x)+y $

functions functional-equations

Find the limit given that $f(1)=1$, $f(x+y)=f(x)+f(y)+2xy$ and $f\left(\frac{1}{x}\right)=\frac{f(x)}{x^4}$

algebra-precalculus limits functional-equations

Find all function $f(n)$ satisfying $f(n)^2 = n f(f(n))$

algebra-precalculus functions functional-equations

How can prove this equation.

trigonometry functional-equations

Continuous function satisfying $f^{k}(x)=f(x^k)$

real-analysis functional-equations

Find all functions $f:\mathbb{R}^+\to \mathbb{R}$ such that $xf(xf(x)-4)-1=4x$

real-analysis contest-math functional-equations

Solve functional equation $ h(y)+h^{-1}(y)=2y+y^2 $

physics functional-equations inverse-function

Determine all functions satisfying $f(x + f(x + y)) + f(xy) = x + f(x + y) +yf(x)$

contest-math functional-equations

Find all functions with $f(x + y) + f(x - y) = 2 f(x) f(y)$ and $\lim\limits_{x\to\infty}f(x)=0$.

contest-math functional-equations