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

摘要

For g is an element of C((D) over bar), phi is an element of C(T) and f* is an element of C(T), let BH phi,g,f* (D) be the class of all complex-valued functions f is an element of C-4(D) satisfying Delta(Delta f) = g in the unit disk D with Delta f = phi in the unit circle T and f = f* in T, where Delta f is the Laplacian of f. In this article, we will show that several Schwarz type lemmas for f is an element of BH phi,g,f* (D), and, by applying these results, we will establish a Landau type theorem on a subclass of BH phi,g,f* (D). (C) 2019 Elsevier Masson SAS. All rights reserved.