THE CONVERGENCE OF <i>q</i>-BERNSTEIN POLYNOMIALS (0 &lt; <i>q</i> &lt; 1) AND LIMIT <i>q</i>-BERNSTEIN OPERATORS IN COMPLEX DOMAINS

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2009

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Rocky Mt Math Consortium

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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

Due to the fact that the convergence properties of q-Bernstein polynomials are not similar to those in the classical case q = 1, their study has become an area of intensive research with a wide scope of open problems and unexpected results. The present paper is focused on the convergence of q-Bernstein polynomials, 0 < q < 1, and related linear operators in complex domains. An analogue of the classical result on the simultaneous approximation is presented. The approximation of analytic functions With the help of the limit q-Bernstein operator is studied.

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q-integers, q-binomial coefficients, q-Bernstein polynomials, uniform convergence

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1

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39

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4

Start Page

1279

End Page

1291

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https://doi.org/10.1216/RMJ-2009-39-4-1279
 https://hdl.handle.net/20.500.14411/978

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