Summary: Let \(I\subset \mathbb{R}\) be a nonvoid open interval and \(r\neq 0,1\), \(q\in(0,1)\), such that \(r\neq q\), \(r\neq \frac {1}{2}\) and \(q\neq \frac{1}{2}\). In this paper, we give all the functions \(f,g:I\to\mathbb{R}_+\) such that \[ f\left(\frac{x+y}{2}\right)\left[r(1-q)g(y)-(1-r)qg(x)\right]=\frac{r-q}{1-2q} \left[(1-q)f(x)g(y)-qf(y)g(x)\right] \] for all \(x,y\in I\).