GENERALIZED ROPER-SUFFRIDGE OPERATOR FOR ε STARLIKE AND BOUNDARY STARLIKE MAPPINGS

• 作者: Jie WANG Jianfei WANG
• 来源期刊: 数学物理学报（英文版）
• 年，卷（期）: 2020,（6）
• 页码范围: 1753-1764
• 页数: 12页
• 语种: 英文

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 e starlikeness on the open unit ball of a complex Banach space C× 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 α on the unit ball Bn of Cn, we prove that the Roper-Suffridge extension operator preserves almost boundary starlikeness of order a on Bn. Finally, we propose some problems.