单叶p -调和映射

数学物理学报 ›› 2012, Vol. 32 ›› Issue (3): 588-600.

单叶p -调和映射

乔金静^1,2|王仙桃²

1.河北大学数学与计算机学院河北保定 071002;
2.湖南师范大学数学与计算机科学学院长沙 410081

收稿日期:2010-11-22 修回日期:2011-10-15 出版日期:2012-06-25 发布日期:2012-06-25
基金资助:
国家自然科学基金(11071063)资助

On p-harmonic Univalent Mappings

QIAO Jin-Jing^1,2, WANG Xian-Tao²

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

摘要/Abstract

摘要：

主要目的是介绍两个p -调和映射类HS_p和HC_p及其相应的子类HS_p⁰和HC_p⁰, 同时研究这些类中映射的性质. 首先, 讨论了HS_p⁰和HC_p⁰中映射的几何性质. 证明了在HS_p⁰和HC_p⁰中的映射下, 单位圆盘的像域分别是星形的和凸的. 其次, 确定了HS_p⁰、HC_p⁰、HS_p∩T_p和HC_p∩T_p的极值点, 其中T_p表示具有非负系数的p -调和映射类. 最后, 证明了HC_p中映射邻域的存在性.

关键词: p -调和映射, 星形性, 凸性, 极值点, 邻域

Abstract:

In this paper, the main aim is to introduce two classes HS_p and HC_p of p-harmonic mappings together with their corresponding subclasses HS_p⁰ and HC_p⁰, and investigate the properties of the mappings in these classes. First, we discuss the geometric properties of mappings belonging to HS_p⁰ and HC_p⁰, respectively. We prove that the image domains of the unit disk D under the mappings in HS_p⁰ (resp. HC_p⁰) are starlike (resp. convex). Secondly, extreme points for classes HS_p⁰, HC_p⁰, HS_p∩T_p and HC_p∩T_p are determined, where T_p denotes the set of all p-harmonic mappings with nonnegative coefficients. Finally, we establish the existence of the neighborhoods of mappings in HC_p.

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

中图分类号:

30C65

乔金静, 王仙桃. 单叶p -调和映射[J]. 数学物理学报, 2012, 32(3): 588-600.

QIAO Jin-Jing, WANG Xian-Tao. On p-harmonic Univalent Mappings[J]. Acta mathematica scientia,Series A, 2012, 32(3): 588-600.

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