On the Lupas <i>q</i>-transform

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Date

2011

Authors

Ostrovska, Sofiya

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Pergamon-elsevier Science Ltd

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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

The Lupas q-transform emerges in the study of the limit q-Lupas operator. The latter comes out naturally as a limit for a sequence of the Lupas q-analogues of the Bernstein operator. Lately, it has been studied by several authors from different perspectives in mathematical analysis and approximation theory. This operator is closely related to the q-deformed Poisson probability distribution, which is used widely in the q-boson operator calculus. (Lambda(q)f)(z) := 1/(-z; q)(infinity) . Sigma(infinity)(k=0) f(1 - q(k))q(k(k-1)/2)/(q; q)(k) z(k). In this paper, we study some analytic properties of (Lambda(q)f)(z). In particular, we examine the conditions under which Lambda(q)f can either be an entire function, or a rational one. (C) 2010 Elsevier Ltd. All rights reserved.

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q-integers, q-binomial theorem, Lupas q-analogue of the Bernstein operator, Analytic function, Meromorphic function

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8

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Volume

61

Issue

3

Start Page

527

End Page

532

URI

https://doi.org/10.1016/j.camwa.2010.11.025
 https://hdl.handle.net/20.500.14411/1565

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