On the eigenvectors of the <i>q</i>-Bernstein operators

Abstract

In this article, both the eigenvectors and the eigenvalues of the q-Bernstein operators have been studied. Explicit formulae are presented for the eigenvectors, whose limit behavior is determined both in the case 0<q<1 and in the case q>1. Because the classical case, where q=1, was investigated exhaustively by S. Cooper and S. Waldron back in 2000, the present article also discusses the related similarities and distinctions with the results in the classical case. Copyright (c) 2013 John Wiley & Sons, Ltd.