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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 73 Issue: 3

On the eigenstructure of the q-Stancu operator

Övgü Gürel Yılmaz(RECEP TAYYIP ERDOGAN UNIVERSITY)0000-0003-1498-8526
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Publication Date
2024-09-27
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⚡ TL;DR(Too Long; Didn't Read)

In addition, for special choices of parameters, several eigenfunctions are depicted.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The main goal of this research is to find the eigenvalues and the corresponding eigenfunctions of the q-Stancu operator, $L_{n,s,q}$, introduced by $L$.
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Key Findings & Data:Further, it has been proved that $L_{n,s,q}$ possesses $n − s + 1$ linearly independent eigenfunctions whose explicit expression and the corresponding eigenvalues are derived.
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Conclusion & Impact:In addition, for special choices of parameters, several eigenfunctions are depicted.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:q-integers · q-Stirling numbers · q-Stancu operators

Abstract

The main goal of this research is to find the eigenvalues and the corresponding eigenfunctions of the q-Stancu operator, $L_{n,s,q}$, introduced by $L$. Yun and R. Wang. In this work, an explicit representation for moments of all orders has been derived. Further, it has been proved that $L_{n,s,q}$ possesses $n − s + 1$ linearly independent eigenfunctions whose explicit expression and the corresponding eigenvalues are derived. In addition, for special choices of parameters, several eigenfunctions are depicted.

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Cite This Article

Yılmaz, Ö. G. (2024). On the eigenstructure of the q-Stancu operator. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 73 Issue: 3. https://doi.org/10.31801/cfsuasmas.1388792

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