Year: 2024
Type: preprint
Abstract: A harmonic mapping $f=h+\overline{g}$ in $\mathbb{D}$ is $φ$-normal if $f^{\#}(z)=\mathcal{O}(|φ(z)|), \text{ as } |z|\to 1^-,$ where $f^{\#}(z)={(|h'(z)|+|g'(z)|)}/{(1+|f(z)|^2)}.$ In this paper, we establish several sufficient conditions for harmonic mappings to be $φ$-normal. We also extend the five-point theorem of Lappan for $φ$-normal harmonic mappings.
Source: arXiv (Cornell University)
Authors: Bohra, Nisha, Datt, Gopal, Pal, Ritesh
Institution: Babasaheb Bhimrao Ambedkar University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4402387069