List questions from functional-equations | MathQA

Which functions $f$ satisfy $f(x-a-c)f(x-b)=\alpha f(x-c-\tfrac{a+b}{2})f(x-\tfrac{a+b}{2})$ for every $x$ where $a,b,c,\alpha$ are constants?

Published on 27 Mar 2026 - 18:27

Functional equations: $f(x^3) = \frac{1}{3}f(x)$ and $g(x/b) = b^{a}g(x)$ (uniqueness)

Published on 26 Mar 2026 - 16:07

What are Bottcher coordinates useful for?

Published on 09 Apr 2026 - 2:30

To find inverse of a linear operator

Published on 11 Apr 2026 - 1:42

A question on the existence of an equation about non-autonomous semigroup

Published on 11 Apr 2026 - 20:20

A real-valued function $f$ satisfies the relation $f(x)f(y)=f(2xy+3)+3f(x+y)-3f(y)+6y$, for all real numbers $x$ and $y$, then the value of $f(8)$ is?

Published on 25 Apr 2021 - 10:03

Functional equation with just a small part i can't understand

Published on 12 Apr 2026 - 15:20

Symmetric functional equation $ x f ( y ) + y f ( x ) = ( x + y ) f \left( x ^ 2 + y ^ 2 \right) $ on $ \mathbb N _ 0 $: how to show $ f$ is constant?

Published on 26 Apr 2021 - 0:54

Proof of Cauchy's functional equation

Published on 10 Apr 2026 - 12:00

Functional equation for Rankin-Selberg L functions in the imprimitive case

Published on 25 Mar 2026 - 23:53

Prove that there exists a unique function $f: [0, \infty) \to [0, \infty)$ which satisfies the equation $f(f(x))=6x-f(x)$

Published on 30 Apr 2021 - 19:29

$g(x)h(x)=x$ for odd $g(x)$ and even $h(x)$

Published on 12 Apr 2026 - 18:07

Function inequality : $h(x)=2x$

Published on 09 Apr 2026 - 13:42

Verification of my solution of the functional equation $ f \left( x + y ^ 2 \right) = f ( x ) +f ( y ) ^ 2 $

Published on 01 May 2021 - 14:11

Check the proof by Cauchy's: existence of a function satisfying $ f ( x ) + f ( 2 x ) + \dots + f ( n x ) = 0 $, and $ f ( x ) = 0 $ iff $ x = 0 $

Published on 01 May 2021 - 19:45