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

Abstract

We give coefficient estimates for a class of close-to-convex harmonic mappings, and discuss the Fekete-Szegő problem of it. We also introduce two classes of polyharmonic mappings ${\mathcal{H}\mathcal{S}}_p$ and ${\mathcal{H}\mathcal{C}}_p$, consider the starlikeness and convexity of them, and obtain coefficient estimates on them. Finally, we give a necessary condition for a mapping $F$ to be in the class ${\mathcal{H}\mathcal{C}}_p$.

14 pages, 2 figures

References in corpus (1)

• On polyharmonic univalent mappings