The Bohr's phenomenon for certain K-quasiconformal harmonic mappings

The primary objective of this paper is to establish several sharp versions of improved Bohr inequalities, refined Bohr inequalities, and Bohr-Rogosinski inequalities for the class of $K$-quasiconformal sense-preserving harmonic mappings $f=h+\bar{g}$ in the unit disk $\mathbb{D}:=\{z\in \mathbb{C}:\mathrm{\mid }z\mathrm{\mid }<1\}$, where $f$ and $g$ are analytic functions in $\mathbb{D}$.