Bohr inequalities via proper combinations for a certain class of close-to-convex harmonic mappings

Let H () be the class of complex-valued functions harmonic in and each f=h+g H (), where h and g are analytic. In the study of Bohr phenomenon for certain class of harmonic mappings, it is to find a constant rf (0, 1) such that the inequality align* Mf (r): =r+₍=₂^ (|aₙ|+|bₙ|) rⁿ d (f (0), ) \;for\;|z|=r rf, align* where d (f (0), ) is the Euclidean distance between f (0) and the boundary of: =f (D). The largest such radius rf is called the Bohr radius and the inequality Mf (r) d (f (0), ) is called the Bohr inequality for the class H (). In this paper, we study Bohr phenomenon for the class of close-to-convex harmonic mappings establishing several inequalities. All the results are proved to be sharp.