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New posts in functional-equations
Functions satisfying $\sum_{n=0}^k(-1)^n\binom{k}{k-n}f^{k-n}(x)=0$.
real-analysis
functional-equations
Solve $f^2(x)=x+f(x+1)$
functional-equations
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 $
functional-equations
What is the function $f(x)$ which is differentiable everywhere and $f(x-1)f(x-2)+1=f(x)$?
real-analysis
calculus
functional-equations
Find all functions $f:\mathbb{R}^+\to \mathbb{R}^+$ such that for all $x,y\in\mathbb{R}^+$, $f(x)f(yf(x))=f(x+y)$
real-analysis
analysis
functions
contest-math
functional-equations
How to solve the functional equation $ f(f(x))=ax^2+bx+c $
functional-analysis
functions
functional-equations
An eely function $\mu (n):\;\;\prod\limits_{k = 0}^{n - 1} {\left( {\mu (n) - \mu (k)} \right)} = 1$
functional-analysis
functional-equations
recursion
Find all functions $f$ such that $f(f(x)) - xf(x)=0$
functional-equations
Parallelogram law functional equation: $ f ( x + y ) + f ( x - y ) = 2 \big( f ( x ) + f ( y ) \big) $
real-analysis
recreational-mathematics
functional-equations
Finding Symmetry Group $S_3$ in a function
abstract-algebra
group-theory
complex-analysis
finite-groups
functional-equations
How find this function $f(x)$
ordinary-differential-equations
functional-equations
First order differential equation involving inverse function
ordinary-differential-equations
functional-equations
Solving functional equation $f(4x)-f(3x)=2x$
functional-equations
$f\circ g(x)$ and $g\circ f(x)$ are given; find $f$ and $g$
functional-equations
When does $f(X) = g(X+1)-g(X)$ where $f, g \in \mathbb{C}(X)$?
abstract-algebra
complex-analysis
functional-equations
rational-functions
How find this function $f(1+xy)=f(x)f(y)+f(x+y)$
contest-math
functional-equations
Functional equation: $R(1/x)/x^2 = R(x) $
functional-equations
The existence of bounded linear functional on a complex Hilbert space
functional-analysis
functional-equations
Solve the functional equation $\frac{f(x)}{f(y)}=f\left( \frac{x-y}{f(y)} \right)$
functional-equations
Functional equation $ f(x) + f\left(1-\frac{1}{x}\right) = \tan^{-1}(x) $ and definite integral
calculus
trigonometry
definite-integrals
functional-equations
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