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Generalized Roper-Suffridge Operator for ϵ Starlike and Boundary Starlike Mappings

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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 ϵ 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 α on Bn. Finally, we propose some problems.

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Authors and Affiliations

  1. School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, China

    Jie Wang & Jianfei Wang

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  1. Jie Wang
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  2. Jianfei Wang
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Correspondence to Jianfei Wang.

Additional information

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.

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Wang, J., Wang, J. Generalized Roper-Suffridge Operator for ϵ Starlike and Boundary Starlike Mappings. Acta Math Sci 40, 1753–1764 (2020). https://doi.org/10.1007/s10473-020-0610-y

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  • DOI: https://doi.org/10.1007/s10473-020-0610-y

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