New posts in functional-equations

Functional Equation (no. of solutions): $f(x+y) + f(x-y) = 2f(x) + 2f(y)$

functional-equations bilinear-form

Find all function satisfying $f(f(n))+f(n)=2n+3k$

functions recurrence-relations functional-equations

Is continuity required in order to show that a function satisfying $f(x+y)=f(x)+f(y)$ is of the form $f(x)=cx$? [duplicate]

real-analysis analysis functional-analysis functional-equations

Functional equations $f(x+y)= f(x) + f(y)$ and $f(xy)= f(x)f(y)$

real-analysis functional-equations

If $f(1)=1$, then is it true that $f(n)=n$ for all $n \in \mathbb{N}\cup\{0\}$.

functional-equations

$f(x^2) = xf(x)$ implies that $ f(x) = mx$?

functional-equations

Find all functions $f(x+y)=f(x^{2}+y^{2})$ for positive $x,y$

analysis functions contest-math functional-equations

How are Zeta function values calculated from within the Critical Strip?

complex-analysis number-theory functional-equations riemann-zeta zeta-functions

Real Analysis Proofs: Additive Functions

real-analysis functional-equations

An IMO inspired problem

contest-math functional-equations

Functional Equation $f(mn)=f(m)f(n)$.

contest-math functional-equations

References about Sierpinski's Theorem regarding Darboux functions

real-analysis reference-request functional-equations

How to find $f(x)$, if $f(x)+f(1/x)=f(x)f(1/x)$? [duplicate]

analysis functions polynomials functional-equations

How can I determine the best relationship for 3 variables, given several data points?

statistics functional-equations statistical-inference correlation data-analysis

The functional equation $f(x) + f\bigl(x+f(y)\bigr) = y + f\Bigl(f(x) + f\bigl(f(y)\bigr)\Bigr)$

functional-equations

If $f:\mathbb{R}\to\mathbb{R}$ is continuous and $f(x)\neq x$ for all $x$, must it be true that $f(f(x))\neq x$ for all $x$?

real-analysis general-topology continuity functional-equations

determine all polynomials $P(x)$ such that $(x+1)P(x-1)-(x-1)P(x)$ is a constant polynomial

polynomials contest-math functional-equations

Determine all functions satisfying $f\left ( f(x)^{2}y \right )=x^{3}f(xy)$

algebra-precalculus contest-math functional-equations rational-numbers

Solution to $1-f(x) = f(-x)$

algebra-precalculus functional-equations

$f(x)f(1/x)=f(x)+f(1/x)$

analysis functions polynomials functional-equations