New posts in functional-equations

Functions satisfying $\sum_{n=0}^k(-1)^n\binom{k}{k-n}f^{k-n}(x)=0$.

Solve $f^2(x)=x+f(x+1)$

Finding all functions $ f : \mathbb R \to \mathbb R $ satisfying $ f ( x ) f ( y ) + f ( x y ) + f ( x ) + f ( y ) = f ( x + y ) + 2 x y $

What is the function $f(x)$ which is differentiable everywhere and $f(x-1)f(x-2)+1=f(x)$?

Find all functions $f:\mathbb{R}^+\to \mathbb{R}^+$ such that for all $x,y\in\mathbb{R}^+$, $f(x)f(yf(x))=f(x+y)$

How to solve the functional equation $ f(f(x))=ax^2+bx+c $

An eely function $\mu (n):\;\;\prod\limits_{k = 0}^{n - 1} {\left( {\mu (n) - \mu (k)} \right)} = 1$

Find all functions $f$ such that $f(f(x)) - xf(x)=0$

Parallelogram law functional equation: $ f ( x + y ) + f ( x - y ) = 2 \big( f ( x ) + f ( y ) \big) $

Finding Symmetry Group $S_3$ in a function

How find this function $f(x)$

First order differential equation involving inverse function

Solving functional equation $f(4x)-f(3x)=2x$

$f\circ g(x)$ and $g\circ f(x)$ are given; find $f$ and $g$

When does $f(X) = g(X+1)-g(X)$ where $f, g \in \mathbb{C}(X)$?

How find this function $f(1+xy)=f(x)f(y)+f(x+y)$

Functional equation: $R(1/x)/x^2 = R(x) $

The existence of bounded linear functional on a complex Hilbert space

Solve the functional equation $\frac{f(x)}{f(y)}=f\left( \frac{x-y}{f(y)} \right)$

Functional equation $ f(x) + f\left(1-\frac{1}{x}\right) = \tan^{-1}(x) $ and definite integral