Landau-Type Theorems for Certain Bounded Biharmonic Mappings

摘要

In this paper, we establish three sharp versions of the Landautype theorems for bounded biharmonicmappings F(z) = vertical bar z|(2) G(z)+ H(z), where G(z) and H(z) are harmonic in the unit disk U with G(0) = H(0) = 0 and lambda(F)(0) = parallel to F-z(0)vertical bar - F-<(zover bar>(0)parallel to = 1. Our results generalize (or improve) the corresponding results given in Liu et al. (Math Methods Appl Sci 40: 2582-2595, 2017). Three conjectures for the sharp version of the Landau-type theorem for certain bounded biharmonic mappings are given in third section.