Bohr Phenomenon for $K$-Quasiconformal harmonic mappings and Logarithmic Power Series

Abstract

In this article, we establish the Bohr inequalities for the sense-preserving $K$-quasiconformal harmonic mappings defined in the unit disk $\mathbb{D}$ involving classes of Ma-Minda starlike and convex univalent functions, usually denoted by ${\mathcal{S}}^{\ast }(\psi )$ and $\mathcal{C}(\psi )$ respectively, and for $\log (f(z)/z)$ where $f$ belongs to the Ma-Minda classes or satisfies certain differential subordination. We also estimate Logarithmic coefficient's bounds for the functions in $\mathcal{C}(\psi )$ for the case $\psi (\mathbb{D})$ be convex.

arXiv comment17 pages