Geometric Studies and the Bohr Radius for Certain Normalized Harmonic Mappings

Let H be the class of harmonic functions f = h + (g) over bar in the unit disk D := {z is an element of C : vertical bar z vertical bar < 1}, where h and g are analytic in D. In 2020, N. Ghosh and V. Allu introduced the class P-H(0) ( M) of normalized harmonic mappings defined by P-H(0)(M) = {f = h + (g) over bar is an element of H : Re(zh '' (z)) > - M + vertical bar zg '' (z)vertical bar with M > 0, g ' (0) = 0, z is an element of D}. In this paper, we investigate various geometric properties such as starlikeness, convexity, convex combination and convolution for functions in the class P-H(0)(M). Furthermore, we determine the sharp Bohr-Rogosinski radius, improved Bohr radius and refined Bohr radius for the class P-H(0)(M).