Landau-Type Theorems for Certain Biharmonic Mappings

Abstract EN

Let F(z)=|z|2g(z)+h(z) (|z|<1) be a biharmonic mapping of the unit disk ?, where g and h are harmonic in ?.

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.