  In this paper, we first investigate coefficient estimates for bounded
polyharmonic mappings in the unit disk $\mathbb{D}$. Then, we obtain two
versions of Landau's theorem for polyharmonics mapping $F$, and for the
mappings of the type $L(F)$, where $L$ is the differential operator of
Abdulhadi, Abu Muhanna and Khuri. Examples and numerical estimates are given.
