Improved Bohr's phenomenon in quasi-subordination classes

Recently the present authors established refined versions of Bohr's inequality in case bounded analytic functions. In this article, we state and prove a generalization these results. Here, consider image origin boundary unit disk under function question let distance between both play central role our theorems. Thereby extend Bohr for class quasi-subordinations which contains classes majorization subordination as special cases. As consequence, type theorems functions subordinate to convex or univalent