Schwarz type Lemmas and a Landau type theorem of functions satisfying the biharmonic equation

Abstract

For g∈C(D‾), φ∈C(T) and f⁎∈C(T), let BHφ,g,f⁎(D) be the class of all complex-valued functions f∈C4(D) satisfying Δ(Δf)=g in the unit disk D with Δf=φ in the unit circle T and f=f⁎ in T, where Δf is the Laplacian of f. In this article, we will show that several Schwarz type lemmas for f∈BHφ,g,f⁎(D), and, by applying these results, we will establish a Landau type theorem on a subclass of BHφ,g,f⁎(D).