Schwarz-Type Lemma, Landau-Type Theorem, and Lipschitz-Type Space of Solutions to Inhomogeneous Biharmonic Equations

The purpose of this paper is to study the properties of the solutions to the inhomogeneous biharmonic equations: $$\Delta (\Delta f)=g$$ , where g : $$\overline{\mathbb {D}}\rightarrow \mathbb {C}$$ is a continuous function and $$\overline{\mathbb {D}}$$ denotes the closure of the unit disk $$\mathbb {D}$$ in the complex plane $$\mathbb {C}$$ . In fact, we establish the following properties for those solutions: Firstly, we establish the Schwarz-type lemma. Secondly, by using the obtained results, we get a Landau-type theorem. Thirdly, we discuss their Lipschitz-type property.