Acta mathematica scientia,Series A ›› 2012, Vol. 32 ›› Issue (3): 588-600.

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On p-harmonic Univalent Mappings

 QIAO Jin-Jing1,2, WANG Xian-Tao2   

  1. 1.Department of Mathematics, Hebei University, Hebei Baoding 071002;
    2.Department of Mathematics, Hunan Normal University, Changsha 410081
  • Received:2010-11-22 Revised:2011-10-15 Online:2012-06-25 Published:2012-06-25
  • Supported by:

    国家自然科学基金(11071063)资助

Abstract:

In this paper, the main aim is to introduce two classes HSp and HCp of p-harmonic mappings together with their corresponding subclasses HSp0 and HCp0, and investigate the properties of the mappings in these classes. First, we discuss the geometric properties of mappings belonging to HSp0 and HCp0, respectively. We prove that the image domains of the unit disk D under the mappings in HSp0 (resp. HCp0) are starlike (resp. convex). Secondly, extreme points for classes HSp0, HCp0, HSpTp and HCpTp are determined, where Tp denotes the set of all p-harmonic mappings with nonnegative coefficients. Finally, we establish the existence of the neighborhoods of mappings in HCp.

Key words: p-harmonic mapping, Starlikeness, Convexity, Extreme point, Neighborhood

CLC Number: 

  • 30C65
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