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