New posts in functional-equations

Functions with $\mathrm s(x)^n+ \mathrm c(x)^n \equiv 1$

integration functions indefinite-integrals special-functions functional-equations

$f\left(\frac{2z}{1+z^2}\right)=\left(1+z^2\right)f(z)$, solve $f$.

functions functional-equations

Prove that $f'$ exists for all $x$ in $R$ if $f(x+y)=f(x)f(y)$ and $f'(0)$ exists

analysis derivatives functional-equations

Functions that satisfy $f(x+y)=f(x)f(y)$ and $f(1)=e$

real-analysis elementary-set-theory functional-equations axiom-of-choice

A function satisfying $f \left ( \frac 1 {f(x)} \right ) = x$ [duplicate]

functions functional-equations inverse-function

$f(a)-f(b)$ is rational iff $f(a-b) $ is rational

real-analysis continuity functional-equations rational-numbers fixed-point-theorems

Find $f'(0)$ if $f(x)+f(2x)=x\space\space\forall x$

calculus real-analysis functional-equations

Riemann's thinking on symmetrizing the zeta functional equation

analysis math-history functional-equations riemann-zeta

Find all the function that satisfy : $f\left(\frac{xf(y)}{2}\right)+f\left(\frac{yf(x)}{2}\right)=4xy$

functional-equations

Determine all functions $f(x)$ such that $f(f(x+y))=f(x)+f(y)$

contest-math functional-equations

Prove that if a particular function is measurable, then its image is a rect line [duplicate]

measure-theory functional-equations

Find the integral $\int_{0}^{1} f(x)dx$ for $f(x)+f(1-{1\over x})=\arctan x\,,\quad \forall \,x\neq 0$.

calculus integration functional-equations

How would I prove that this function is affine if $f(x+h)-f(x)=hf'(x)$?

real-analysis functional-equations

Evaluating $f(x) f(x/2) f(x/4) f(x/8) \cdots$

sequences-and-series functional-equations infinite-product

What was this theorem called

trigonometry terminology functional-equations

How to find if this function is always zero?

functions derivatives functional-equations

Does there exist a nontrivial rational function which satisfies $f(f(f(f(x))))=x$?

functional-equations rational-functions

Find all functions such that $f\left(x^2+y\right)=f(x)^2+\frac{f(xy)}{f(x)}$ in $\mathbb R^*$

functional-equations

Find all real polynomials $p(x)$ that satisfy $\sin( p(x) ) = p( \sin(x) )$

real-analysis polynomials functional-equations

Decomposing an intensity spectrum as a superposition of blackbody spectra

functional-analysis physics functional-equations integral-transforms