Landau-type theorems for certain biharmonic mappings (Q1725287)

Summary: Let \(F(z) = | z |^2 g(z) + h(z) (| z | < 1)\) be a biharmonic mapping of the unit disk \(\mathbb{D}\), where \(g\) and \(h\) are harmonic in \(\mathbb{D}\). In this paper, the Landau-type theorems for biharmonic mappings of the form \(L(F)\) are provided. Here \(L\) represents the linear complex operator \(L = (z \partial / \partial z) - \overline{(z} \partial / \partial \overline{z)}\) defined on the class of complex-valued \(C^1\) functions in the plane. The results, presented in this paper, improve the related results of earlier authors.