Bohr-type inequalities for unimodular bounded analytic functions

Abstract: 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.