New posts in functional-equations

Can every real function be represented as two shifted even functions?

functions functional-equations

Periodicity of a Function Given the Functional Equation $f(x+a)=\frac12+\sqrt{f(x)-\big(f(x)\big)^2}$ [closed]

functions functional-equations periodic-functions

Functional equation $f(px)+p=[f(x)]^2$

real-analysis functions continuity functional-equations nonlinear-analysis

A possible solution to $\sqrt {5-x}=5-x^2$ (without taking square from both sides)

algebra-precalculus polynomials solution-verification radicals functional-equations

Trying to understand pathological solution(s) to $f:f\rightarrow f$

set-theory functional-equations infinity

When is $f^{-1}=1/f\,$?

reference-request functions functional-equations

Cauchy functional equation with non choice

functional-equations axiom-of-choice

$f(16x)=16f(x) $ and $ f$ is continuous

functions continuity functional-equations

How to find the function $f$ given $f(f(x)) = 2x$?

calculus functional-equations

Functional Equation $f(x+y)=f(x)+f(y)+f(x)f(y)$

functional-equations

Nowhere continuous functions $f: \mathbb{R} \to \mathbb{R}$ such that $f\bigl(f(x)\bigr) = \frac{f(2x)}{2}$ [closed]

real-analysis calculus functions continuity functional-equations

Solution to the functional equation $f(2x) = f(x)\cdot\sin(x)$?

real-analysis functions fourier-analysis functional-equations

A function such that $f(f(n)) = -n$?

functional-equations

Find all the functions $f: \mathbb{N} \to \mathbb{N} $ such that $(m+f(n))(n+f(m))$ is a perfect square for all $m,n$

contest-math functional-equations

Functions whose derivative is the inverse of that function [duplicate]

ordinary-differential-equations functional-equations

If $f: \Bbb{R}\rightarrow\Bbb{R}$ is continuous at $0$ and $f(x)=f(2x)$ for each $x\in\Bbb{R}$ then $f$ is constant.

calculus continuity functional-equations

Characterization of continuous functions with the property $f(x) = f\left(\frac{x}{1-x}\right)$ [closed]

real-analysis functions continuity functional-equations

A Functional Differential Equation: $f^\prime(x) =\frac{f(2x)}{2f(x)}$

calculus ordinary-differential-equations trigonometry functional-equations

If $f(x)=g(x)f(h(x))$ with $g$ and $h$ known, can I obtain $f$?

calculus functional-equations

Polynomials $P(x)\in k[x]$ satisfying condition $P(x^2)=P(-x)P(x)$

combinatorics polynomials field-theory extension-field functional-equations