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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
An application for inverse functions is also given.
📌 3 Key Takeaways
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Objective & Hypothesis:The $k-$ Fibonacci numbers $F_{k,n}\:(k>0)$, defined recursively by $F_{k,0}=0$ , $F_{k,1}=1$ and $F_{k,n}=kF_{k,n}+F_{k,n-1}$ for $n\geq1$ are used to define a new class $\mathcal{S}\mathcal{L}^k$.
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Key Findings & Data:The purpose of this paper is to apply properties of $k$-Fibonacci numbers to consider the classical problem of estimation of the Fekete–Szegö problem for the class $\mathcal{S}\mathcal{L}^{k}$.
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Conclusion & Impact:An application for inverse functions is also given.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:univalent functions · convex functions · starlike functions
Abstract
The $k-$ Fibonacci numbers $F_{k,n}\:(k>0)$, defined recursively by $F_{k,0}=0$ , $F_{k,1}=1$ and $F_{k,n}=kF_{k,n}+F_{k,n-1}$ for $n\geq1$ are used to define a new class $\mathcal{S}\mathcal{L}^k$. The purpose of this paper is to apply properties of $k$-Fibonacci numbers to consider the classical problem of estimation of the Fekete–Szegö problem for the class $\mathcal{S}\mathcal{L}^{k}$. An application for inverse functions is also given.
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Cite This Article
ÖZGÜR, N. Y., RAİNA, R. K., SOKÓŁ, J. (2022). Applications of $k$-Fibonacci numbers for the starlike analytic functions. Hacettepe Journal of Mathematics and Statistics, Cilt: 44 - Sayı: 1, 121–127. https://ajindex.com/articles/530281