On the Image of the Limit <i>q</I>-bernstein Operator

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2009

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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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The limit q-Bernstein operator B-q emerges naturally as an analogue to the Szasz-Mirakyan operator related to the Euler distribution. Alternatively, B-q comes out as a limit for a sequence of q-Bernstein polynomials in the case 0<q<1. Lately, different properties of the limit q-Bernstein operator and its iterates have been studied by a number of authors. In particular, it has been shown that B-q is a positive shape-preserving linear operator on C[0, 1] with parallel to B-q parallel to = 1, which possesses the following remarkable property: in general, it improves the analytic properties of a function. In this paper, new results on the properties of the image of B-q are presented. Copyright (C) 2009 John Wiley & Sons, Ltd.

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limit q-Bernstein operator, q-Bernstein polynomials, uniform convergence, power series, analytic function

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32

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15

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1964

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1970

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https://doi.org/10.1002/mma.1118
 https://hdl.handle.net/20.500.14411/1536

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