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

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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 \(\mathbb {C}^n\).

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Acknowledgements

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

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Authors and Affiliations

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

    Ming-Sheng Liu & Fen Wu

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  1. Ming-Sheng Liu
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  2. Fen Wu
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Correspondence to Ming-Sheng Liu.

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Communicated by Saminathan Ponnusamy.

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Liu, MS., Wu, F. Sharp Inequalities of Homogeneous Expansions of Almost Starlike Mappings of Order Alpha. Bull. Malays. Math. Sci. Soc. 42, 133–151 (2019). https://doi.org/10.1007/s40840-017-0472-1

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  • DOI: https://doi.org/10.1007/s40840-017-0472-1

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