  In this paper, we establish three new versions of Landau-type theorems for
bounded bi-analytic functions of the form $F(z)=\bar{z}G(z)+H(z)$, where $G$
and $H$ are analytic in the unit disk $|z|<1$ with $G(0)=H(0)=0$ and $H'(0)=1$.
In particular, two of them are sharp while the other one either generalizes or
improves the corresponding result of Abdulhadi and Hajj. As consequences,
several new sharp versions of Landau-type theorems for certain subclasses of
bounded biharmonic mappings are proved.
