Improved Bohr's phenomenon in quasi-subordination classes

Abstract

Recently the present authors established refined versions of Bohr's inequality in the case of bounded analytic functions. In this article, we state and prove a generalization of these results in a reformulated "distance form" version and thereby we extend the refined versions of the Bohr inequality for the class of the quasi-subordinations which contains both the classes of majorization and subordination as special cases. As a consequence, we obtain several new results.