New posts in functional-equations

Why is every such function constant: $f(x)=f(x^2)$ for $x \in [0,1]$?

continuity functional-equations

d'Alembert-like functional equation: $f(x+y)+g(x-y)=\lambda f(x)g(y)$

functional-equations

Find all bijections $\,\,f:[0,1]\rightarrow[0,1],\,$ which satisfy $\,\,f\big(2x-f(x)\big)=x$.

calculus recreational-mathematics contest-math functional-equations recursion

Solving functional equation $f(x+y)+f(x-y)=2f(x)\cos y$?

functions trigonometry functional-equations

About the addition formula $f(x+y) = f(x)g(y)+f(y)g(x)$

functions trigonometry arithmetic functional-equations

I am searching for an unusual real-valued function.

functions functional-equations

If $f$ is continuous and $f(x+y) = f(x)+f(y)$, then $f(x) = cx$ for all $x \in \mathbb{R}$

real-analysis continuity functional-equations

non-continuous function satisfies $f(x+y)=f(x)+f(y)$

real-analysis analysis functional-analysis functional-equations

2015 Brazilian Math Olympiad Number theory problem

elementary-number-theory contest-math functional-equations

Find $f(x)$ where $ f(x)+f\left(\frac{1-x}x\right)=x$

calculus algebra-precalculus functional-equations

Solving $f(yf(x)+x/y)=xyf(x^2+y^2)$ over the reals

contest-math functional-equations

very elementary proof of Maxwell's theorem

probability-distributions functional-equations

Find all functions $f: \mathbb N \rightarrow \mathbb N$ such that $f(n!)=f(n)!$

functional-equations

Functions $f$ satisfying $ f\circ f(x)=2f(x)-x,\forall x\in\mathbb{R}$.

calculus real-analysis functional-equations

Show a function for which $f(x + y) = f(x) + f(y) $ is continuous at zero if and only if it is continuous on $\mathbb R$

real-analysis continuity functional-equations

Solution of Cauchy functional equation which has an antiderivative

real-analysis functional-equations

If $f:[0,\infty)\to [0,\infty)$ and $f(x+y)=f(x)+f(y)$ then prove that $f(x)=ax$

calculus analysis functional-equations

Prove that function is constant

functional-equations

Differentiable functions satisfying $f'(f(x))=f(f'(x))$

real-analysis functional-equations problem-solving

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

analysis functional-equations