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On the roper-suffridge extension operator

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Abstract

In 1995, Roper and Suffridge defined an extension operator which maps a locally biholomorphic function on the unit diskD in ℂ to a locally biholomorphic mapping on the unit ballB n in ℂn. This extension operator preserves many important properties, e.g., convexity and starlikeness, etc. In this note, we introduce the family ofε starlike mappings, and prove that the Roper-Suffridge extension operator preserves theε starlikeness on some Reinhardt domains. This result includes many known results and solves an open problem of Graham and Kohr.

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Authors and Affiliations

  1. Department of Mathematics, University of Science and Technology of China Hefei, 230026, Anhui, P. R. China

    Sheng Gong & Taishun Liu

Authors
  1. Sheng Gong
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  2. Taishun Liu
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Corresponding author

Correspondence to Sheng Gong.

Additional information

Project supported by the National Science Foundation of China.

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Gong, S., Liu, T. On the roper-suffridge extension operator. J. Anal. Math. 88, 397–404 (2002). https://doi.org/10.1007/BF02786583

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  • DOI: https://doi.org/10.1007/BF02786583

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