Landau’s theorem for certain biharmonic mappings

In this paper, we show the existence of Landau and Bloch constants for biharmonic mappings of the form L(F)L(F). Here L   represents the linear complex operator L=z∂∂z-z¯∂∂z¯ defined on the class of complex-valued C1C1 functions in the plane, and F   belongs to the class of biharmonic mappings of the form F(z)=|z|2G(z)+K(z)(|z|<1)F(z)=|z|2G(z)+K(z)(|z|<1), where G and K are harmonic.