On Bohr's inequality for special subclasses of stable starlike harmonic mappings

The focus of this article is to explore the Bohr inequality for a specific subset of harmonic starlike mappings introduced by Ghosh and Vasudevarao (Some basic properties of certain subclass of harmonic univalent functions, Complex Var. Elliptic Equ. 63 (2018), no. 12, 1687-1703.). This set is denoted as B-H(0)(M)& colone;{f = h + g is an element of H-0 : divided by zh ''(z)divided by <= M - divided by zg ''(z)divided by} for z is an element of D, where 0 < M <= 1. It is worth mentioning that the functions belonging to the class B-H(0)(M) are recognized for their stability as starlike harmonic mappings. With this in mind, this research has a twofold goal: first, to determine the optimal Bohr radius for this specific subclass of harmonic mappings, and second, to extend the Bohr-Rogosinski phenomenon to the same subclass.