The Sharpness of Convergence Results for <i>q</I>-bernstein Polynomials in The Case <i>q</I> &gt; 1

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2008

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Springer Heidelberg

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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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Due to the fact that in the case q > 1 the q-Bernstein polynomials are no longer positive linear operators on C[0, 1], the study of their convergence properties turns out to be essentially more difficult than that for q 1. In this paper, new saturation theorems related to the convergence of q-Bernstein polynomials in the case q > 1 are proved.

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q-integers, q-binomial coefficients, q-Bernstein polynomials, uniform convergence, analytic function, Cauchy estimates

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Q4

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Volume

58

Issue

4

Start Page

1195

End Page

1206

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https://doi.org/10.1007/s10587-008-0079-7
 https://hdl.handle.net/20.500.14411/1030

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