Characterizing Rotationally Typically Real Logharmonic Mappings
Complex Variables
2017-10-05 v1
Abstract
This paper treats the class of normalized logharmonic mappings f(z) = zh(z)bar{g(z)} in the unit disk satisfying {\phi}(z) = zh(z)g(z) is analytically typically real. Every such mapping f is shown to be a product of two particular logharmonic mappings, each of which admits an integral representation. Also obtained is the radius of starlikeness and an upper estimate for arclength. Additionally, it is shown that f maps the unit disk into a domain symmetric with respect to the real axis when it is univalent and its second dilatation has real coefficients.
Keywords
Cite
@article{arxiv.1710.01443,
title = {Characterizing Rotationally Typically Real Logharmonic Mappings},
author = {Najla M. Alarifi and Zayid Abdulhadi and Rosihan M. Ali},
journal= {arXiv preprint arXiv:1710.01443},
year = {2017}
}