Coefficient problem for some class of functions nonvanishing in the unit disk

In this paper we determine the bounds of the functional $b_2-\alpha b_1, \alpha$-real, for holomorphic univalent and bounded functions, symmetric with respect to the real axis, nonvanishing in the unit disk. The result generalized the estimates of $b_1$ and $b_2$ for these functions, obtained by Sladkowska [4].