ON THE RATE OF CONVERGENCE FOR THE <i>q</i>-DURRMEYER POLYNOMIALS IN COMPLEX DOMAINS

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On the rate of convergence for the MASLO_2024_OG_SO_MT.pdf (278.83 KB)

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2024

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Walter de Gruyter Gmbh

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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 q-Durrmeyer polynomials are one of the popular q-versions of the classical operators of approximation theory. They have been studied from different points of view by a number of researchers. The aim of this work is to estimate the rate of convergence for the sequence of the q-Durrmeyer polynomials in the case 0 < q < 1. It is proved that for any compact set D subset of C, the rate of convergence is O(q(n)) as n -> infinity. The sharpness of the obtained result is demonstrated.

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q-integers, q-Durrmeyer operator, limit q-Durrmeyer operator, rate of convergence, analytic function

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74

Issue

5

Start Page

1267

End Page

1276

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https://doi.org/10.1515/ms-2024-0092
 https://hdl.handle.net/20.500.14411/10243

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