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Journals / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 4

On the eigenstructure of the $(\alpha,q)$-Bernstein operator

Bülent Köroğlu
Fatma Taşdelen Yeşildal
Pages
1111–1122
Publication Date
2022-10-18
DOI
—
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⚡ TL;DR(Too Long; Didn't Read)

Moreover, we will give the asymptotic behaviour of these eigenvalues and eigenvectors for all $q>0.$ Some eigenvectors for various values of $\alpha$ and $q$ are depicted.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The eigenvalues and eigenvectors of $(\alpha,q)$-Bernstein operators are unknown and not studied in the literature.
📊
Key Findings & Data:As the main result of this article, the eigenvalues and eigenvectors of $(\alpha,q)$-Bernstein operators are obtained.
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Conclusion & Impact:Moreover, we will give the asymptotic behaviour of these eigenvalues and eigenvectors for all $q>0.$ Some eigenvectors for various values of $\alpha$ and $q$ are depicted.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:q-calculus · q)-Bernstein polynomials · Eigenvalues

Abstract

The eigenvalues and eigenvectors of $(\alpha,q)$-Bernstein operators are unknown and not studied in the literature. As the main result of this article, the eigenvalues and eigenvectors of $(\alpha,q)$-Bernstein operators are obtained. Moreover, we will give the asymptotic behaviour of these eigenvalues and eigenvectors for all $q>0.$ Some eigenvectors for various values of $\alpha$ and $q$ are depicted.

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Cite This Article

Köroğlu, B., Yeşildal, F. T. (2022). On the eigenstructure of the $(\alpha,q)$-Bernstein operator. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 4, 1111–1122. https://ajindex.com/articles/529979

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