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Journals / Turkish Journal of Mathematics / 2020 / Cilt: 44 - Sayı: 4

Faber polynomial coefficients for certain subclasses of analytic and biunivalent functions

Abdel Moneim LASHIN
Fatma Z. EL-EMAM
Pages
1345–1361
Publication Date
2022-11-05
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The results, which are presented in this paper, wouldgeneralize those in related earlier works of several authors.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we introduce and investigate two new subclasses of analytic and bi-univalent functions definedin the open unit disc.
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Key Findings & Data:We use the Faber polynomial expansions to find upper bounds for the nth (n ≥ 3) TaylorMaclaurin coefficients |$a_n$| of functions belong to these new subclasses with $a_k$ = 0 for 2 ≤ k ≤ n − 1, also we findnon-sharp estimates on the first two coefficients |$a_2$| and |$a_3$|.
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Conclusion & Impact:The results, which are presented in this paper, wouldgeneralize those in related earlier works of several authors.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, we introduce and investigate two new subclasses of analytic and bi-univalent functions definedin the open unit disc. We use the Faber polynomial expansions to find upper bounds for the nth (n ≥ 3) TaylorMaclaurin coefficients |$a_n$| of functions belong to these new subclasses with $a_k$ = 0 for 2 ≤ k ≤ n − 1, also we findnon-sharp estimates on the first two coefficients |$a_2$| and |$a_3$|. The results, which are presented in this paper, wouldgeneralize those in related earlier works of several authors.

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Cite This Article

LASHIN, A. M., EL-EMAM, F. Z. (2022). Faber polynomial coefficients for certain subclasses of analytic and biunivalent functions. Turkish Journal of Mathematics, Cilt: 44 - Sayı: 4, 1345–1361. https://ajindex.com/articles/607547

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