A Functional Equation with Differences


Gyula Maksa




Let $R$ denote the set of real number. Let us determine all functions $f:R\rightarrow R$ such that $$\frac{f(tx+ty(-f(tx)}{f(tx)-f(tx-ty)}=\frac{f(x+y)-f(x)}{f(x)-f(x-y)}$$ for all $x,y,t\in R,\;\;yt\neq 0$. This problem is due to P. Drṟeve{a}gilṟeve{a} [1].