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Sufficient Criteria for \(\varepsilon \) Starlike Mappings in a Complex Banach Space

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Abstract

Several sufficient conditions for \(\varepsilon \) starlike mappings on the unit ball \(B\) in a complex Banach space are provided. From these, we may construct many concrete \(\varepsilon \) starlike mappings on \(B\). Furthermore, several growth results associated with these sufficient conditions are also provided.

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Acknowledgments

This paper was written while the first author visited Rutgers University-Camden, he thanks Rutgers University for hospitality, he also thanks Professor Siqi Fu for his helpful discussion and encouragement. The authors thank the referee for his/her helpful comments and suggestions to improve our manuscript.

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Authors and Affiliations

  1. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, Guangdong, People’s Republic of China

    Ming-Sheng Liu

  2. Department of Mathematics, Fuzhou University, Fuzhou, 350108, Fujian, People’s Republic of China

    Yu-Can Zhu

Authors
  1. Ming-Sheng Liu
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  2. Yu-Can Zhu
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Correspondence to Ming-Sheng Liu.

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Communicated By: J. E. Fornaess.

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Liu, MS., Zhu, YC. Sufficient Criteria for \(\varepsilon \) Starlike Mappings in a Complex Banach Space. Complex Anal. Oper. Theory 7, 607–622 (2013). https://doi.org/10.1007/s11785-012-0243-9

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  • DOI: https://doi.org/10.1007/s11785-012-0243-9

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