LANDAU-TYPE THEOREMS for CERTAIN BOUNDED BI-ANALYTIC FUNCTIONS and BIHARMONIC MAPPINGS

In this paper, we establish three new versions of Landau-Type theorems for bounded bi-Analytic functions of the form F(z) = zG(z) + H(z), where G and H are analytic in the unit disk with G(0) = H(0) = 0 and H0(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.