Starlikeness and convexity of polyharmonic mappings

Abstract

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

References in corpus (1)

• Radius of Close-to-convexity of Harmonic Functions