Landau-type theorems for certain bounded bi-analytic functions and biharmonic mappings

Abstract

In this article, we establish three new versions of Landau-type theorems for bounded bi-analytic functions of the form $F(z)=\bar {z}G(z)+H(z)$ , where G and H are analytic in the unit disk with $G(0)=H(0)=0$ and $H'(0)=1$ . In particular, two of them are sharp, while the other one either generalizes or improves the corresponding result of Abdulhadi and Hajj. As consequences, several new sharp versions of Landau-type theorems for certain subclasses of bounded biharmonic mappings are proved.