  In this note we give sufficient conditions for bivariate, homogeneous,
symmetric means $M$ and $N$ to satisfy Ky Fan inequalities
$$\frac{M}{M'}<\frac{N}{N'}\qquad\text{ and }\quad
\frac{1}{M}-\frac{1}{M'}<\frac{1}{N}-\frac{1}{N'}.$$
