On polyharmonic univalent mappings

Abstract

In this paper, we introduce a class of complex-valued polyharmonic mappings, denoted by $H{S}_p(\lambda )$, and its subclass $H{S}_p^0(\lambda )$, where $\lambda \in [0,1]$ 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 $H{S}_p(\lambda )$ and $H{S}_p^0(\lambda )$, showing that the mappings in $H{S}_p(\lambda )$ are univalent and sense preserving. We also prove that the mappings in $H{S}_p^0(\lambda )$ are starlike with respect to the origin, and characterize the extremal points of the above classes.

References in corpus (1)

• Radius of Close-to-convexity of Harmonic Functions

Cited by in corpus (3)

• On lengths, areas and Lipschitz continuity of polyharmonic mappings
• Geometric properties of $\log$-polyharmonic mappings
• Coefficient estimates and the Fekete-Szeg\H o problem for certain classes of polyharmonic mappings