On the <i>q</I>-bernstein Polynomials of Piecewise Linear Functions in the Case <i>q</I> &gt; 1

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2013

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Pergamon-elsevier Science Ltd

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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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The aim of this paper is to present new results related to the approximation of continuous functions by their q-Bernstein polynomials in the case q > 1. The first part of the paper is devoted to the behavior of the q-Bernstein polynomials of piecewise linear functions. This study naturally leads to the notion of truncated q-Bernstein polynomials introduced in the paper. The second part deals with the asymptotic estimates for the norms of the m-truncated q-Bernstein polynomials, in the case where both n and q vary. The results of the paper are illustrated by numerical examples. (C) 2012 Elsevier Ltd. All rights reserved.

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q-integers, q-binomial coefficients, q-Bernstein polynomials, q-Bernstein operator, Operator norm

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57

Issue

9-10

Start Page

2419

End Page

2431

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https://doi.org/10.1016/j.mcm.2012.01.022
 https://hdl.handle.net/20.500.14411/444

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