Landau-Type Theorems for Certain Biharmonic Mappings - Ming-Sheng Liu; Zhen-Xing Liu; Jun-Feng Xu (Abstract and Applied Analysis)
Let F(z)=|z|2g(z)+h(z)  (|z|<1) be a biharmonic mapping of the unit disk 𝔻, where g and h are harmonic in 𝔻. In this paper, the Landau-type theorems for biharmonic mappings of the form L(F) are provided. Here L represents the linear complex operator L=(z∂/∂z)-(z¯∂/∂z)¯ defined on the class of complex-valued C1 functions in the plane. The results, presented in this paper, improve the related results of earlier authors.