Starlikeness and convexity of polyharmonic mappings

In this paper, we first find an estimate for the range of polyharmonic mappings in the class $HC_{p}^{0}$. Then, we obtain two characterizations in terms of the convolution for polyharmonic mappings to be starlike of order $α$, and convex of order $β$, respectively. Finally, we study the radii of starlikeness and convexity for polyharmonic mappings, under certain coefficient conditions.

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