New posts in functional-equations

How to prove that the functional equation $f(x)+f(y)=f(\frac{xf'(x)+yf'(y)}{f'(x)+f'(y)})+f(\frac{x+y}2)$ is verified only by some basic functions?

real-analysis functional-equations

Function whose inverse is also its derivative?

ordinary-differential-equations functional-equations

How to obtain $f(x)$, if it is known that $f(f(x))=x^2+x$?

functions functional-equations

Which functions satisfy $f^n(x) = f(x)^n$ for some $n \ge 2$?

functions functional-equations function-and-relation-composition

Mean value theorem functional equation: $ f ' \left ( \frac { x + y } 2 \right ) = \frac { f ( x ) - f ( y ) } { x - y } $

calculus functional-equations

Interesting functional equations problem? $f(x) + 3 f\left( \frac {x-1}{x} \right) = 7x$

algebra-precalculus functional-equations

Help in solving a simple functional equation: $3f(2x+1)=f(x) + 5x$

functional-equations

Cauchy type equation in three variables: $ P(x) + P(y) + P(z) = P(x + y + z)$ when $xy + yz + zx = 1$

functional-equations

Different functional equations than Cauchy type? $2f(xy)=f(x)+f(y)$

functional-equations

Find $f(x)$ such that $f(f(x)) = x^2 - 2$

contest-math functional-equations

Looking for a function such that...

functional-analysis functions functional-equations

Graph of discontinuous additive function is dense in $ \mathbb R ^ 2 $

real-analysis functional-equations

A function in which addition and multiplication behave the same way

functions functional-equations

continuous functions on $\mathbb R$ such that $g(x+y)=g(x)g(y)$ [duplicate]

real-analysis functions functional-equations

I need to find all functions $f:\mathbb R \rightarrow \mathbb R$ which are continuous and satisfy $f(x+y)=f(x)+f(y)$

real-analysis functional-equations

Proving that an additive function $f$ is continuous if it is continuous at a single point

calculus functional-equations

Can there be an injective function whose derivative is equivalent to its inverse function?

real-analysis functions functional-equations inverse-function

thoughts about $f(f(x))=e^x$

calculus real-analysis functional-equations tetration

Find $f: \mathbb{N_0} \to \mathbb{N_0}$ which satisfies $f^n(x+f(y))=f^{n+1}(x)+f^n(y) \text{ for } n \in \mathbb{N}.$

functional-equations

3rd iterate of a continuous function equals identity function

calculus real-analysis functional-equations function-and-relation-composition