On the eigenstructure of the q-Stancu operator

Year 2024, Volume: 73 Issue: 3, 820 - 832, 27.09.2024

Övgü Gürel Yılmaz

https://doi.org/10.31801/cfsuasmas.1388792

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.

Keywords

q-integers, q-Stirling numbers, q-Stancu operators, moments, eigenvalues, eigenfunctions

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