Year: 2013
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Chen, Jiaolong, Rasila, Antti, Wang, Xiantao
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1560272500