Radius of fully starlikeness and fully convexity of harmonic linear differential operator

Let f = h + g be a normalized harmonic mapping in the unit disk D. In this paper, we obtain the sharp radius of univalence, fully starlikeness and fully convexity of the harmonic linear differential operators (Formula presented) when the coefficients of h and g satisfy harmonic Bieberbach coefficients conjecture conditions. Similar problems are also solved when the coefficients of h and g satisfy the corresponding necessary conditions of the harmonic convex function f = h + g. All results are sharp. Some of the results are motivated by the work of Kalaj et al. [8].