Bohr radius for certain classes of close-to-convex harmonic mappings

Let H be the class of harmonic functions f = h + g ¯ in the unit disk D : = { z ∈ C : | z | < 1 } , where h and g are analytic in D . Let P H 0 ( α ) = { f = h + g ¯ ∈ H : Re ( h ′ ( z ) - α ) > | g ′ ( z ) | with 0 ≤ α < 1 , g ′ ( 0 ) = 0 , z ∈ D } be the class of close-to-convex mappings defined by Li and Ponnusamy (Nonlinear Anal 89:276–283, 2013). In this paper, we obtain the sharp Bohr–Rogosinski radius, improved Bohr radius and refined Bohr radius for the class P H 0 ( α ) .