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 φ ={φ _n(r)}^∞_n=0 in place of the {r^n}^∞_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.