ON CERTAIN CLASSES OF P-HARMONIC MAPPINGS

摘要

A p times continuously diffrentiable complex-valued function F in a domain D ?C is p-harmonic, if F satisfies the p-harmonic equation △. .△F=0, where p (≥1) is an integer and △ represents the complex Laplacian operator. In this paper, the main aim is to introduce two classes MHp (α) and NHp (α) of p-harmonic mappings together with their subclasses MHp (α)∩T1 and MHp (α)∩T2, NHp (α)∩T2, and investigate the properties of mappings in these classes. First, we obtain characterizations for mappings in MHp (α)∩T1 and NHp ((α)∩T2 in terms of S-Inequality-I and S-Inequality-II, respectively. And then we prove that the image domains of the unit disk D under the mappings in MHp (α) (resp. NHp (α) satisfying Inequality-I (resp. Inequality-II) are starlike (resp. Convex) of certain order.