This is equivalent to the following result: If all critical points of a rational function lie on a circle in the Riemann sphere (for example, on the real line), then the function maps this circle into ...

Extending a result of Khavinson and $\acute {S}wi\cedil {a}tek$ (2003) we show that the rational harmonic function $\overline {r (z)} - z$, where r (z) is a rational function of degree n > 1, has no ...