Newbetuts

Analytic solution of the functional equation $V\left(z^d\right)=dz^{d-1} V(z)+\sum_{k=2}^d b_k z^{d-k}$

Functions $f: \mathbb{Z}^{+}\to \mathbb{R}$ satisfying $x f(y) + y f(x) = (x+y) f(x^2+y^2)$

Solve the functional equation $f(xy) = f(x)f(y) - f(x + y) + 1$ and $f(1) = 2$

Solution to the functional equation $f(a+b)=\sum_{k=0}^{n-1}f^{(n-1-k)}(a)f^{(k)}(b)$

How to find $f:\mathbb{Q}^+\to \mathbb{Q}^+$ if $f(x)+f\left(\frac1x\right)=1$ and $f(2x)=2f\bigl(f(x)\bigr)$ [duplicate]

A functional equation problem on $\mathbb{Q}^{+}$: $f(x)+f\left(\frac{1}{x}\right)=1$ and $f(2x)=2f\bigl(f(x)\bigr)$

Functional equation in natural numbers with divisibility: $f(m) + f(n) + mn \ | \ m^2f(m) + n^2f(n) + f(m)f(n)$

$f\colon\mathbb{R}\to\mathbb{R}$ such that $f(x)+f(f(x))=x^2$ for all $x$?

Are Exponential and Trigonometric Functions the Only Non-Trivial Solutions to $F'(x)=F(x+a)$?

Which $f$ satisfy the equation $\,\,f(x)\,f(y)-f(x+y)=\sin x\,\sin y\,$?

A possible converse to the Cayley-Hamilton theorem?

Are all multiplicative functions additive?

How to show that $f$ is a straight line if $f(\frac{x+y}{2})=\frac{f(x)+f(y)}{2}$?

Solution(s) to $f(x + y) = f(x) + f(y)$ (and miscellaneous questions...)

Class of integrals: $I(a)=\int_0^\infty \frac{dx}{e^x+ax}$

A question concerning on the axiom of choice and Cauchy functional equation

Is there a real-valued function $f$ such that $f(f(x)) = -x$? [duplicate]

New posts in functional-equations

A real function which is additive but not homogenous

Find all functions that satisfy $f(\frac{x+4}{1-x}) + f(x) = x$

A functional equation with no solution

Analytic solution of the functional equation $V\left(z^d\right)=dz^{d-1} V(z)+\sum_{k=2}^d b_k z^{d-k}$

Functions $f: \mathbb{Z}^{+}\to \mathbb{R}$ satisfying $x f(y) + y f(x) = (x+y) f(x^2+y^2)$

Solve the functional equation $f(xy) = f(x)f(y) - f(x + y) + 1$ and $f(1) = 2$

Solution to the functional equation $f(a+b)=\sum_{k=0}^{n-1}f^{(n-1-k)}(a)f^{(k)}(b)$

How to find $f:\mathbb{Q}^+\to \mathbb{Q}^+$ if $f(x)+f\left(\frac1x\right)=1$ and $f(2x)=2f\bigl(f(x)\bigr)$ [duplicate]

A functional equation problem on $\mathbb{Q}^{+}$: $f(x)+f\left(\frac{1}{x}\right)=1$ and $f(2x)=2f\bigl(f(x)\bigr)$

Functional equation in natural numbers with divisibility: $f(m) + f(n) + mn \ | \ m^2f(m) + n^2f(n) + f(m)f(n)$

$f\colon\mathbb{R}\to\mathbb{R}$ such that $f(x)+f(f(x))=x^2$ for all $x$?

Are Exponential and Trigonometric Functions the Only Non-Trivial Solutions to $F'(x)=F(x+a)$?

Which $f$ satisfy the equation $\,\,f(x)\,f(y)-f(x+y)=\sin x\,\sin y\,$?

A possible converse to the Cayley-Hamilton theorem?

Are all multiplicative functions additive?

How to show that $f$ is a straight line if $f(\frac{x+y}{2})=\frac{f(x)+f(y)}{2}$?

Solution(s) to $f(x + y) = f(x) + f(y)$ (and miscellaneous questions...)

Class of integrals: $I(a)=\int_0^\infty \frac{dx}{e^x+ax}$

A question concerning on the axiom of choice and Cauchy functional equation

Is there a real-valued function $f$ such that $f(f(x)) = -x$? [duplicate]