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Mathematics in Computer Science

Erschienen in:

04.07.2019

Bounds on Initial Coefficients for a Certain New Subclass of Bi-univalent Functions by Means of Faber Polynomial Expansions

verfasst von: F. Müge Sakar, S. Melike Aydoğan

Erschienen in: Mathematics in Computer Science | Ausgabe 3/2019

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Abstract

In this paper, we present a new subclass \({\mathcal {T}}_{\varSigma }(\mu )\) of bi univalent functions belong to \(\varSigma \) in the open unit disc \({\mathcal {U}} =\left\{ z\, :\,\,z\in {\mathcal {C}}\,\,and \,\, |z| <1\right\} \). Then, we use the concepts of Faber polynomial expansions to find upper bound for the general coefficient of such functions belongs to the defined class. Further, for the functions in this subclass we obtain bound on first three coefficients \(|a_{2}|\), \(|a_{3}|\) and \(|a_{4}|\). We hope that this paper will inspire future researchers in applying our approach to other related problems.

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Titel: Bounds on Initial Coefficients for a Certain New Subclass of Bi-univalent Functions by Means of Faber Polynomial Expansions
verfasst von: F. Müge Sakar
S. Melike Aydoğan
Publikationsdatum: 04.07.2019
Verlag: Springer International Publishing
Erschienen in: Mathematics in Computer Science / Ausgabe 3/2019
Print ISSN: 1661-8270
Elektronische ISSN: 1661-8289
DOI: https://doi.org/10.1007/s11786-019-00406-7

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