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

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2014

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Wiley

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Mathematics
(2000)
The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.

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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.

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Turan, Mehmet/0000-0002-1718-3902
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Turan, Mehmet ORCID logo

Keywords

q-integers, q-binomial coefficients, q-Bernstein operator, eigenvalues, eigenvectors

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8

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Q1

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Volume

37

Issue

4

Start Page

562

End Page

570

URI

https://doi.org/10.1002/mma.2814
 https://hdl.handle.net/20.500.14411/209

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