Landau-Bloch theorems for bounded biharmonic mappings

Abstract

We determine coefficient bounds for bounded planar biharmonic mappings and generalize the Landau-Bloch univalency theorems for such bounded biharmonic functions. The univalence radii presented here improve many related results published to date, including the most recent one [Complex Var. Elliptic Equ. 58(12) (2013), 1667-1676] and are sharp in some given cases.