Note on Weighted Bohr's Inequality

In this paper, first we give a new generalization of the Bohr’s inequality for the class of bounded analytic functions ${\mathcal{B}}^{\mathcal{\prime }}$ and for the class of sense-preserving $K$-quasiconformal harmonic mappings of the form $f=h+\bar{g},$ where $h\in {\mathcal{B}}^{\mathcal{\prime }}\mathrm{.}$ Finally we give a new generalization of the Bohr’s inequality for the class of analytic functions subordinate to univalent functions and for the class of sense-preserving $K$-quasiconformal harmonic mappings of the form $f=h+\bar{g},$ where $h$ is subordinated to some analytic function.