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On the eigenvectors of the q ‐Bernstein operators
Author(s) -
Ostrovska S.,
Turan M.
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2814
Subject(s) - eigenvalues and eigenvectors , mathematics , limit (mathematics) , pure mathematics , algebra over a field , mathematical analysis , quantum mechanics , physics
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.