Improved Bohr inequalities for certain class of harmonic univalent functions

Let H be the class of complex-valued harmonic mappings f = h + (g) over bar defined in the unit disk D := {z is an element of C : vertical bar z vertical bar < 1}, where h and g are analytic functions in D with the normalization h(0) = 0 = h'(0) - 1 and g(0) = 0. Let H-0 = {f = h + <(g)over bar> is an element of H: g'(0) = 0}. Let P-H(0)(M) := {f = h+ (g) over bar is an element of H-0 : Re (zh '' (Z))( > -M + vertical bar Zg ''(z)vertical bar, z is an element of D and M > 0}.) be the class of harmonic univalent mappings in the unit disk D, [Ghosh N, Allu V. On some subclasses of harmonic mappings. Bull Aust Math Soc. 2020;101:130-140.]. In this paper, we obtain the sharp Bohr-Rogosinski inequality, improved Bohr inequality, refined Bohr inequality and Bohr-type inequality for the class P-H(0)(M).