Bohr phenomenon for locally univalent functions and logarithmic power series

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 $K\to \mathrm{\infty }$. One of the results includes the sharpened version of a theorem by Kayumov $\mathit{\text{et.}}\mathit{\text{al.}}$ ($\mathit{\text{Math.}}\mathit{\text{Nachr.}}$, 291 (2018), no. 11–12, 1757–1768). In addition Bohr inequalities have been established for uniformly locally univalent holomorphic functions, and for $\log (f(z)\mathrm{/}z)$ where $f$ is univalent or inverse of a univalent function.