# Bohr phenomenon for locally univalent functions and logarithmic power series

## TL;DR

This paper establishes Bohr inequalities for various classes of harmonic and univalent functions, including quasiconformal harmonic mappings and locally univalent holomorphic functions, extending and sharpening previous results.

## Contribution

It introduces new Bohr inequalities for sense-preserving quasiconformal harmonic mappings and locally univalent functions, improving existing theorems and covering broader function classes.

## Key findings

- Bohr inequalities for sense-preserving $K$-quasiconformal harmonic mappings.
- Sharpened version of a theorem by Kayumov et al.
- Bohr inequalities for locally univalent holomorphic functions and for $ ext{log}(f(z)/z)$.

## Abstract

In this article we prove Bohr inequalities for sense-preserving $K$-quasiconformal harmonic mappings defined in $\mathbb{D}$ and obtain the corresponding results for sense-preserving harmonic mappings by letting $K\to\infty$. One of the results includes the sharpened version of a theorem by Kayumov $\textit{et. al.}$ ($\textit{Math. Nachr.}$, 291 (2018), no. 11--12, 1757--1768). In addition Bohr inequalities have been established for uniformly locally univalent holomorphic functions, and for $\log(f(z)/z)$ where $f$ is univalent or inverse of a univalent function.