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Unified solution of Fekete-Szegö problem for subclasses of starlike mappings in several complex variables

  • Zhenhan Tu and Liangpeng Xiong EMAIL logo
Published/Copyright: July 19, 2019
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Abstract

Let Sψ be a subclass of starlike functions in the unit disk 𝕌, where ψ is a convex function such that ψ(0) = 1, ψ′(0) > 0, ℜ(ψ(ξ)) > 0 and ψ(𝕌) is symmetric with respect to the real axis. We obtain the sharp solution of Fekete-Szegö problem for the family Sψ, and then extend the result to the case of corresponding subclass defined on the bounded starlike circular domain Ω in several complex variables, which give an unified answer of Fekete-Szegö problem for the kinds of subclasses of starlike mappings defined on Ω. At last, we propose two conjectures related the same problems on the unit ball in a complex Banach space and on the unit polydisk in ℂn.

  1. (Communicated by Stanisława Kanas)

Acknowledgement

The project is supported by the National Natural Science Foundation of China (No. 11671306).

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Received: 2018-05-27
Accepted: 2019-02-22
Published Online: 2019-07-19
Published in Print: 2019-08-27

© 2019 Mathematical Institute Slovak Academy of Sciences

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