New posts in Functional Equations

Given $a,b,c$ positive numbers, is there a function $h$ such that $h(ax+b) = c \cdot h(x)$ for all $x>0$?

What are the continuous solutions to the functional equation $f(x) = \tfrac{1}{2}f(x^2)+\tfrac{1}{2}f(2x-x^2)$?

Finding all positive real functions satisfying $xf(y)+f(f(y))\leq f(x+y)$

Does there exist a function $f_{\Box,\Box}(\Box)$ making the formula $a + (b \oplus c) = (f_{b,c}(a)+b) \oplus (f_{c,b}(a)+c)$ true?

Multivariate polynomial functional equation

Find $P(7/8)$ given ${P(5)}^2=P(6)$ and $(x-1)P(x+1)=(x+2)P(x)$

Find all continuous functions in $0$ that $2f(2x) = f(x) + x $

If $f(\frac{x+y}{x-y})=\frac{f(x)+f(y)}{f(x)-f(y)}$, which of the following statement is correct

Find all continuous function $f: \mathbb R \rightarrow \mathbb R$

A functional equation of two variables