The Schwarz type Lemmas and the Landau type theorem of mappings satisfying Poisson's equations

Abstract

For a given continuous function $g:\Omega \to \mathbb{C}$, we establish some Schwarz type Lemmas for mappings $f$ in $\Omega$ satisfying the {\rm PDE}: $\Delta f=g$, where $\Omega$ is a subset of the complex plane $\mathbb{C}$. Then we apply these results to obtain a Landau type theorem, which is a partial answer to the open problem in \cite{CP}. %The obtained results are

19 pages

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