On the Fekete-Szegö problem for classes of bi-univalent functions

In this paper we obtain the Fekete-Szego inequalities for the classes [H.sub.σ] (φ), [ST.sub.σ] (α, φ) and [M.sub.σ] (α, φ) of bi-univalent functions defined in terms of subordination. These inequalities result in the bounds of the third coefficient which improve many known results concerning differ...

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Bibliographic Details
Published in:Bulletin of the Belgian Mathematical Society, Simon Stevin Simon Stevin, 2014-01, Vol.21 (1), p.169-178
Main Author: Zaprawa, Pawel
Format: Article
Language:English
Subjects:
30C45
30C50
Analysis
bi-convex functions
bi-starlike functions
bi-univalent functions
Fekete-Szegö inequality
Functional equations
Functions
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Summary:In this paper we obtain the Fekete-Szego inequalities for the classes [H.sub.σ] (φ), [ST.sub.σ] (α, φ) and [M.sub.σ] (α, φ) of bi-univalent functions defined in terms of subordination. These inequalities result in the bounds of the third coefficient which improve many known results concerning different classes of bi-univalent functions. Key words and phrases : bi-univalent functions, bi-starlike functions, bi-convex functions, Fekete-Szego inequality.
ISSN:1370-1444
2034-1970
DOI:10.36045/bbms/1394544302