数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (6): 1753-1764.doi: 10.1007/s10473-020-0610-y

• 论文 • 上一篇    下一篇

GENERALIZED ROPER-SUFFRIDGE OPERATOR FOR $\epsilon$ STARLIKE AND BOUNDARY STARLIKE MAPPINGS

王洁, 王建飞   

  1. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
  • 收稿日期:2019-07-10 修回日期:2020-04-03 出版日期:2020-12-25 发布日期:2020-12-30
  • 通讯作者: Jianfei WANG,E-mail:jfwang@hqu.edu.cn E-mail:jfwang@hqu.edu.cn
  • 作者简介:Jie WANG,E-mail:wangjie5306@163.com
  • 基金资助:
    The project was partially supported by the NNSF of China (11671362, 11971165), Beijing Municipal Natural Science Foundation (1182008) and the Scientific Research Funds of Huaqiao University.

GENERALIZED ROPER-SUFFRIDGE OPERATOR FOR $\epsilon$ STARLIKE AND BOUNDARY STARLIKE MAPPINGS

Jie WANG, Jianfei WANG   

  1. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
  • Received:2019-07-10 Revised:2020-04-03 Online:2020-12-25 Published:2020-12-30
  • Contact: Jianfei WANG,E-mail:jfwang@hqu.edu.cn E-mail:jfwang@hqu.edu.cn
  • Supported by:
    The project was partially supported by the NNSF of China (11671362, 11971165), Beijing Municipal Natural Science Foundation (1182008) and the Scientific Research Funds of Huaqiao University.

摘要: This article is devoted to a deep study of the Roper-Suffridge extension operator with special geometric properties. First, we prove that the Roper-Suffridge extension operator preserves $\epsilon$ starlikeness on the open unit ball of a complex Banach space $\mathbb{C}\times X$, where $X$ is a complex Banach space. This result includes many known results. Secondly, by introducing a new class of almost boundary starlike mappings of order $\alpha$ on the unit ball $B^n$ of ${\mathbb{C}}^{n}$, we prove that the Roper-Suffridge extension operator preserves almost boundary starlikeness of order $\alpha$ on $B^n$. Finally, we propose some problems.

关键词: Biholomorphic mapping, $\epsilon$ starlikeness, boundary starlikeness

Abstract: This article is devoted to a deep study of the Roper-Suffridge extension operator with special geometric properties. First, we prove that the Roper-Suffridge extension operator preserves $\epsilon$ starlikeness on the open unit ball of a complex Banach space $\mathbb{C}\times X$, where $X$ is a complex Banach space. This result includes many known results. Secondly, by introducing a new class of almost boundary starlike mappings of order $\alpha$ on the unit ball $B^n$ of ${\mathbb{C}}^{n}$, we prove that the Roper-Suffridge extension operator preserves almost boundary starlikeness of order $\alpha$ on $B^n$. Finally, we propose some problems.

Key words: Biholomorphic mapping, $\epsilon$ starlikeness, boundary starlikeness

中图分类号: 

  • 32H02