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Sharp Inequalities of Homogeneous Expansions of Almost Starlike Mappings of Order Alpha

  • Ming-Sheng LiuEmail author
  • Fen Wu
Article
  • 67 Downloads

Abstract

In this paper, we first obtain several sharp inequalities of homogeneous expansion for the subclass of all normalized almost starlike mappings of order \(\alpha \) defined on the unit ball B of a complex Banach space X. Then, with these sharp inequalities, we derive the sharp estimates of the third and fourth homogeneous expansions for the above mappings defined on the unit polydisk \(D^n\) in \(\mathbb {C}^n\).

Keywords

Almost starlike mappings of order \(\alpha \) Inequalities of homogeneous expansions The sharp estimate of the third homogeneous expansions The sharp estimate of the fourth homogeneous expansions 

Mathematics Subject Classification

32A30 32H02 

Notes

Acknowledgements

The research was financially supported by Guangdong Natural Science Foundation (Grant Nos. 2014A030307016, 2014A030313422).

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2017

Authors and Affiliations

  1. 1.School of Mathematical SciencesSouth China Normal UniversityGuangzhouPeople’s Republic of China

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