New posts in functional-equations

The function $f (x) = f \left (\frac x2 \right ) + f \left (\frac x2 + \frac 12\right)$

functional-equations

Are these two series really equal to each other? If so, why?

sequences-and-series complex-analysis functional-equations

Prove that function is continuous without knowing the function explicitly

real-analysis continuity functional-equations

All solutions of $f(x)f(-x)=1$

real-analysis functions functional-equations

Sum of roots of a functional equation

algebra-precalculus functions functional-equations

Functions satisfying $f\left( f(x)^2+f(y) \right)=xf(x)+y$

contest-math functional-equations

Polynomial: $p(x) = p(x+3)$.

polynomials functional-equations

Increasing function $ f : \mathbb R ^ + \to \mathbb R $ with $ x f ( x ) + 2 > 0 $ and $ f ( x ) f \left( f ( x ) + \frac 4 x \right) = 1 $

functions functional-equations

Find $f''(x)$ if $f\circ f'(x) = 4x^2 + 3$

derivatives functional-equations function-and-relation-composition

Functional equation $f(xy)=f(x)+f(y)$ and differentiability

calculus derivatives functional-equations

Find all continuous functions from positive reals to positive reals such that $f(x)^2=f(x^2)$

functional-equations

Problem in solving functional equation $f(x^2 + yf(x)) = xf(x+y)$

functional-equations

Solve the functional equation $f(xf(y)+yf(x))=yf(x)+xf(y)$

functional-equations

Maximising Property

calculus functions optimization functional-equations maxima-minima

Improvement IMO 1988 $f(f(n))=n+1987$

elementary-number-theory functional-equations

Determine whether or not the function f it is bijective 2f(3-2x)+f(3/2-x/2)=x, where x is a real number

functions functional-equations

The easy(?) part of IMO 2011 Problem 3

functional-equations contest-math

Solving Differential Functional Equation $f(2x)=2f(x)f'(x)$

ordinary-differential-equations functional-equations

Find all functions $f:\mathbb N\to \mathbb N$ such that $\frac{4f(x)f(y-3)}{f(x)f(y-2)+f(y)f(x-2)}$ is an integer for all $x>2$ and $y>3$.

elementary-number-theory functions contest-math functional-equations

Solution for exponential function's functional equation by using a definition of derivative

functional-equations