# The starlikeness, convexity, covering theorem and extreme points of p-harmonic mappings

Document Type : Research Paper

Authors

1 Department of Mathematics, Hunan Normal University, Changsha, Hunan 410081, People's Republic of China.

2 Hunan Normal University of China

Abstract

The main
aim of this paper is to introduce three classes $H^0_{p,q}$,
$H^1_{p,q}$ and $TH^*_p$ of $p$-harmonic mappings and discuss the
properties of mappings in these classes. First, we discuss the
starlikeness and convexity of mappings in $H^0_{p,q}$ and
$H^1_{p,q}$. Then establish the covering theorem for mappings in
$H^1_{p,q}$. Finally, we determine the extreme points of the class
$TH^*_{p}$.

Keywords

Main Subjects

### History

• Receive Date: 05 January 2011
• Revise Date: 13 March 2011
• Accept Date: 13 March 2011