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

Year 2021, Volume: 50 Issue: 4, 1111 - 1122, 06.08.2021

Bülent Köroğlu , Fatma Taşdelen Yeşildal

https://doi.org/10.15672/hujms.779544

Cited By: 3

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.

Keywords

q-calculus, (α,q)-Bernstein polynomials, Eigenvalues, Eigenvectors

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