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

Authors : Bülent KÖROĞLU, Fatma TAŞDELEN YEŞİLDAL

Pages : 1111-1122

Doi:10.15672/hujms.779544

View : 25 | Download : 13

Publication Date : 2021-08-06

Article Type : Research Paper

Abstract :The eigenvalues and eigenvectors of $insert ignore into journalissuearticles values(\alpha,q);$-Bernstein operators are unknown and not studied in the literature. As the main result of this article, the eigenvalues and eigenvectors of $insert ignore into journalissuearticles values(\alpha,q);$-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