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Lappan's five-point theorem for {\phi}-Normal Harmonic Mappings
- Publication Year :
- 2024
-
Abstract
- A harmonic mapping $f=h+\overline{g}$ in $\mathbb{D}$ is $\varphi$-normal if $f^{\#}(z)=\mathcal{O}(|\varphi(z)|), \text{ as } |z|\to 1^-,$ where $f^{\#}(z)={(|h'(z)|+|g'(z)|)}/{(1+|f(z)|^2)}.$ In this paper, we establish several sufficient conditions for harmonic mappings to be $\varphi$-normal. We also extend the five-point theorem of Lappan for $\varphi$-normal harmonic mappings.<br />Comment: 10 pages
- Subjects :
- Mathematics - Complex Variables
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2408.05809
- Document Type :
- Working Paper