Bohr-type inequalities for unimodular bounded analytic functions

In this paper, we establish several new versions of Bohr-type inequalities for bounded analytic functions in the unit disk by allowing $\phi =\{{\phi }_n(r){\}}_{n=0}^{\mathrm{\infty }}$ in place of the $\{r^n{\}}_{n=0}^{\mathrm{\infty }}$ 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.