Let \( \mathcal {B}:=\{f(z)=\sum _{n=0}^{\infty }a_nz^n\; \text{ converges } \text{ in }\; \mathbb {D}: |f(z)|<1\; \text{ in }\; \mathbb {D}\} \) . The classical Bohr inequality states that if \( f\in \mathcal {B}\) , then \( \sum _{n=0}^{\infty }|a_n|r^n\le 1\;\;\text{ for }\;\; r\le {1}/{3} \) and the constant 1/3 known as the Bohr radius. In this paper, we obtain an improved version of Bohr inequalities for a subclass \( \mathcal{H}\mathcal{C}_n(\phi ) \) of close-to-convex harmonic mappings, whose analytic parts are Ma-Minda convex functions. Then, we obtain a sharp Bohr inequality for subordination class of bounded harmonic mappings. A function \( f: \mathbb {D}\rightarrow \mathbb {C} \) is said to be log-harmonic if there is a \( w\in \mathcal {B} \) such that f is a non-constant solution of the non-linear elliptic partial differential equation \( \bar{f}_{\bar{z}}(z)/\bar{f}(z)=w(z)f_{z}(z)/f(z). \) We obtain several improved Bohr inequalities for the classes of log-harmonic mappings and starlike log-harmonic mapping. Most of the results obtained in this paper are sharp.
