Korean J. Math. Vol. 32 No. 2 (2024) pp.285-295
DOI: https://doi.org/10.11568/kjm.2024.32.2.285

Faber polynomial coefficient estimates for analytic bi-univalent functions associated with Gregory coefficients

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Published: Jun 30, 2024
Keywords:
Analytic function, bi-univalent function, coefficient estimates, Faber polynomials, Gregory coefficients
Mathematics Subject Classification:
30C45

Main Article Content

Serap Bulut
Kocaeli University, Faculty of Aviation and Space Sciences, Arslanbey Campus, 41285 Kartepe-Kocaeli, Turkey.

Abstract

In this work, we consider the function
Ψ(z)=zln⁡(1+z)=1+∑n=1∞Gnzn
whose coefficients Gn are the Gregory coefficients related to Stirling numbers of the first kind and introduce a new subclass GΣλ,μ(Ψ) of analytic bi-univalent functions subordinate to the function Ψ.


For functions belong to this class, we investigate the estimates for the general Taylor-Maclaurin coefficients by using the Faber polynomial expansions. In certain cases, our estimates improve some of those existing coefficient bounds.



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