On the Sets of Convergence for Sequences of the <i>q</i>-Bernstein Polynomials with <i>q</i> &gt; 1

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2012

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Hindawi Publishing Corporation

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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 convergence of the sequence of the q-Bernstein polynomials {B-n,B-q(f x)} in the case q > 1, where f is a continuous function on [0,1]. It is shown that the polynomials converge to f uniformly on the time scale J(q) = {q(-j)}(j-0)(infinity) boolean OR {0}, and that this result is sharp in the sense that the sequence {B-n,B-q(f;x)}(n-1)(infinity) may be divergent for all x is an element of R \ J(q). Further the impossibility of the uniform approximation for the Weierstrass-type functions is established. Throughout the paper the results are illustrated by numerical examples.

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3

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https://doi.org/10.1155/2012/185948
 https://hdl.handle.net/20.500.14411/1433

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