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We give coefficient estimates for a class of close-to-convex harmonicmappings, and discuss the Fekete-Szeg\H{o} problem of it. We also introduce twoclasses of polyharmonic mappings $\mathcal{HS}_{p}$ and $\mathcal{HC}_{p}$,consider the starlikeness and convexity of them, and obtain coefficientestimates on them. Finally, we give a necessary condition for a mapping $F$ tobe in the class $\mathcal{HC}_{p}$.

Coefficient estimates and the Fekete-Szeg\H o problem for certain classes of polyharmonic mappings