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Results in Mathematics

, 74:141 | Cite as

Janowski-Starlike Mappings of Complex Order \(\lambda \) on the Unit Ball \(B^n\)

  • Xiaofei Li
  • Xiaofei ZhangEmail author
Article
  • 63 Downloads

Abstract

In this paper the authors generalize the notion Janowski-starlike functions of complex order on the unit disk \(\Delta \) to the unit ball \(B^n\) in higher dimensions, written as \(\mathcal {S}^*_{B^n}[A,B, \lambda ]\). The growth and distortion theorems for Janowski-starlike mappings of complex order \(\lambda \) are characterized in Sect. 2. Finally, we prove that if f belongs to a subclass of Janowski-starlike function of complex order on the unit disk \(\Delta \) in \(\mathbb {C}\), then the Roper–Suffridge extension operator and the modified Roper–Suffridge extension operator are all Janowski-starlike mappings of complex order \(\lambda \) on the unit ball \(B^n\) in Sect. 3. Related extension results for \(\mathcal {S}^*_{B^n}[A,B, \lambda ]\) are also given.

Keywords

Growth and distortion theorems Roper–Suffridge extension operator Janowski-starlike mappings 

Mathematics Subject Classification

32A30 30C45 

Notes

Acknowledgements

This work is supported by the National Natural Science Foundation of China (No. 11701307), the Key Scientific Research Projects in Universities of Henan Province (No. 18B110016), the Foster Foundation of Pingdingshan University (No. PXY-PYJJ2016007).

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsPingdingshan UniversityPingdingshanChina

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