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

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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