Bohr radius for some classes of Harmonic mappings
Complex Variables
2020-10-06 v1
Abstract
We introduce a general class of sense-preserving harmonic mappings defined as follows: \begin{equation*} \mathcal{S}^0_{h+\bar{g}}(M):= \{f=h+\bar{g}: \sum_{m=2}^{\infty}(\gamma_m|a_m|+\delta_m|b_m|)\leq M, \; M>0 \}, \end{equation*} where , are analytic functions in and \begin{equation*} \gamma_m,\; \delta_m \geq \alpha_2:=\min \{\gamma_2, \delta_2\}>0, \end{equation*} for all . We obtain Growth Theorem, Covering Theorem and derive the Bohr radius for the class . As an application of our results, we obtain the Bohr radius for many classes of harmonic univalent functions and some classes of univalent functions.
Keywords
Cite
@article{arxiv.2010.01304,
title = {Bohr radius for some classes of Harmonic mappings},
author = {S. Sivaprasad Kumar and Kamaljeet Gangania},
journal= {arXiv preprint arXiv:2010.01304},
year = {2020}
}