Faber Polynomials with common zero

Abstract: We describe the two sets of meromorphic univalent functions in the class $\Sigma$, for which the sequence of Faber polynomials ${F_j}<em>{j=1}^\infty$ have the roots with following properties respectively: $\sum</em>{j=1}^{{n}|F_j(z_0)|=0&lt;|F_{n+1}(z_0)|,} $ $n\in\mathbb N,$ and $|F_1(z_0)|&gt; 0=\sum_{j=2}<sup>{\infty}|F_j(z_0)|$. We found an explicit form of Faber polynomials for such functions.