  In this paper, we introduce a class of complex-valued polyharmonic mappings,
denoted by $HS_{p}(\lambda)$, and its subclass $HS_{p}^{0}(\lambda)$, where
$\lambda\in [0,1]$ is a constant. These classes are natural generalizations of
a class of mappings studied by Goodman in 1950's. We generalize the main
results of Avci and Z{\l}otkiewicz from 1990's to the classes $HS_{p}(\lambda)$
and $HS_{p}^{0}(\lambda)$, showing that the mappings in $HS_{p}(\lambda)$ are
univalent and sense preserving. We also prove that the mappings in
$HS_{p}^{0}(\lambda)$ are starlike with respect to the origin, and characterize
the extremal points of the above classes.
