Volume 37, Issue 4 pp. 562-570
Research Article

On the eigenvectors of the q-Bernstein operators

S. Ostrovska

S. Ostrovska

Department of Mathematics, Atilim University, 06836 Incek Ankara, Turkey

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M. Turan

Corresponding Author

M. Turan

Department of Mathematics, Atilim University, 06836 Incek Ankara, Turkey

Correspondence to: M. Turan, Department of Mathematics, Atilim University, 06836 Incek, Ankara, Turkey.

E-mail: [email protected]

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First published: 28 May 2013
Citations: 7

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 © 2013 John Wiley & Sons, Ltd.

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