MathDB

functional equation with strictly increasing function and f((x+y)/2)

Source: Chile Finals 2008 L2 p3

October 5, 2022

algebrafunctional equationfunction

Problem Statement

Determine all strictly increasing functions

f : R \to R

such that for all

x \ne y

to hold

\frac{2\left[f(y)-f\left(\frac{x+y}{2}\right) \right]}{f(x)-f(y)}=\frac{f(x)-f(y)}{2\left[f\left(\frac{x+y}{2}\right)-f(x) \right]}