The Bohr's Phenomenon involving multiple Schwarz functions

Abstract: The primary objective of this paper is to establish several sharp versions of Bohr inequalities for bounded analytic functions in the unit disk $\mathbb{D} := {z\in\mathbb{C} : |z| < 1}$ involving multiple Schwarz functions. Moreover, we obtain an improved version of the classical Rogosinski inequality for analytic functions in $\mathbb{D}$.