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On the Fekete and Szegö Inequality for a Subclass of Strongly Starlike Mappings of Order \({\varvec{\alpha }}\)

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Abstract

Let \(\mathcal {S}_\alpha ^*\) be the familiar class of strongly starlike functions of order \(\alpha \) in the unit disk. In this paper, first, we prove the following result

$$\begin{aligned} \max \limits _{f\in \mathcal {S}_\alpha ^*}|a_3-\lambda a_2^2|\le \alpha \max \{1,\ \alpha |3-4\lambda |\}, \ \lambda \in \mathbb {C}. \end{aligned}$$

The above estimate is sharp for each \(\lambda \). Second, we generalize this result to several complex variables.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, 330022, China

    Huan Luo & Qinghua Xu

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  1. Huan Luo
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  2. Qinghua Xu
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Correspondence to Qinghua Xu.

Additional information

This work was supported by NNSF of China (Grant Nos. 11561030, 11261022, 11471111), the Jiangxi Provincial Natural Science Foundation of China (Grant Nos. 20152ACB20002, 20161BAB201019), and Natural Science Foundation of Department of Education of Jiangxi Province, China (Grant No. GJJ150301).

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Luo, H., Xu, Q. On the Fekete and Szegö Inequality for a Subclass of Strongly Starlike Mappings of Order \({\varvec{\alpha }}\) . Results Math 72, 343–357 (2017). https://doi.org/10.1007/s00025-017-0650-3

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