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单叶p-调和映射
  • ISSN号：1003-3998
  • 期刊名称：《数学物理学报：A辑》
  • 时间：0
  • 分类：O174.5[理学—数学;理学—基础数学]
  • 作者机构：[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
  • 相关基金：国家自然科学基金(11071063)资助
作者： 乔金静[1,2], 王仙桃[2]
关键词： p, -调和映射, 星形性, 凸性, 极值点, 邻域, p-harmonic mapping Starlikeness Convexity Extreme point Neighborhood
中文摘要：

主要目的是介绍两个p -调和映射类HSp和HCp及其相应的子类HSp0和HCp0, 同时研究这些类中映射的性质. 首先, 讨论了HSp0和HCp0中映射的几何性质. 证明了在HSp0和HCp0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HSp0、HCp0、HSp∩Tp和HCp∩Tp的极值点, 其中Tp表示具有非负系数的p -调和映射类. 最后, 证明了HCp中映射邻域的存在性.

英文摘要：

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, HSp∩Tp and HCp∩Tp 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.

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期刊信息
  • 《数学物理学报：A辑》
  • 北大核心期刊（2011版）
  • 主管单位:中国科学院
  • 主办单位:中国科学院武汉物理与数学研究所
  • 主编：李邦河 陈贵强 朱熹平
  • 地址：湖北省武汉市武昌小洪山西路30号武汉71010信箱
  • 邮编：430071
  • 邮箱：actams@wipm.ac.cn
  • 电话：027-87199206
  • 国际标准刊号：ISSN：1003-3998
  • 国内统一刊号：ISSN：42-1226/O
  • 邮发代号:38-214
  • 获奖情况:
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  • 被引量:5382