Eigenstructure for binomial operators*

Abstract

In this article, the eigenvalues and eigenvectors of positive binomial operators are presented. The results generalize the previously obtained ones related to Bernstein operators. Illustrative examples are supplied.

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

“…Many researchers have studied the eigenstructure of the extensions of Bernstein and q-Bernstein operators. See, for example, [6,7,8,10,21]. The present work is based on the studies by S. Cooper and S. Waldron in 2000 related to the eigenstructure of the classical and multi-variable Bernstein operators [4,5].…”