  In this paper, we establish several new versions of Bohr-type inequalities
for bounded analytic functions in the unit disk by allowing
$\varphi=\{\varphi_n(r)\}^{\infty}_{n=0}$ in place of the
$\{r^n\}^{\infty}_{n=0}$ in the power series representations of the functions
involved with the Bohr sum and thereby introducing a single parameter, which
generalize several related results of earlier authors.
