arXiv subjects
Publications and source records attributed to Jiaolong Chen.
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.
In this paper, we introduce a class of complex-valued polyharmonic mappings, denoted by $HS_{p}(λ)$, and its subclass $HS_{p}^{0}(λ)$, where $λ\in [0,1]$ 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 Złotkiewicz from 1990's to the classes $HS_{p}(λ)$ and $HS_{p}^{0}(λ)$, showing that the mappings in $HS_{p}(λ)$ are univalent and sense preserving. We also prove that the mappings in $HS_{p}^{0}(λ)$ are starlike with respect to the origin, and characterize the extremal points of the above classes.