The <i>q</I>-bernstein Polynomials of the Cauchy Kernel With a Pole on [0,1] in the Case <i>q</I> &gt; 1

dc.authorscopusid 35610828900
dc.authorscopusid 9276702800
dc.authorwosid Ostrovska, Sofiya/AAA-2156-2020
dc.contributor.author Ostrovska, Sofiya
dc.contributor.author Ozban, Ahmet Yasar
dc.contributor.other Mathematics
dc.date.accessioned 2024-07-05T14:28:38Z
dc.date.available 2024-07-05T14:28:38Z
dc.date.issued 2013
dc.department Atılım University en_US
dc.department-temp [Ostrovska, Sofiya; Ozban, Ahmet Yasar] Atilim Univ, Dept Math, TR-06836 Ankara, Turkey en_US
dc.description.abstract The problem to describe the Bernstein polynomials of unbounded functions goes back to Lorentz. The aim of this paper is to investigate the convergence properties of the q-Bernstein polynomials B-n,B-q(f; x) of the Cauchy kernel 1/x-alpha with a pole alpha is an element of [0, 1] for q > 1. The previously obtained results allow one to describe these properties when a pole is different from q(-m) for some m is an element of {0, 1, 2, ...}. In this context, the focus of the paper is on the behavior of polynomials B-n,B-q(f; x) for the functions of the form f(m)(x) = 1/(x - q(-m)), x not equal q(-m) and f(m)(q(-m)) = a, a is an element of R. Here, the problem is examined both theoretically and numerically in detail. (C) 2013 Elsevier Inc. All rights reserved. en_US
dc.identifier.citationcount 3
dc.identifier.doi 10.1016/j.amc.2013.07.034
dc.identifier.endpage 747 en_US
dc.identifier.issn 0096-3003
dc.identifier.issn 1873-5649
dc.identifier.scopus 2-s2.0-84881433938
dc.identifier.startpage 735 en_US
dc.identifier.uri https://doi.org/10.1016/j.amc.2013.07.034
dc.identifier.uri https://hdl.handle.net/20.500.14411/419
dc.identifier.volume 220 en_US
dc.identifier.wos WOS:000324558600070
dc.identifier.wosquality Q1
dc.institutionauthor Ostrovska, Sofiya
dc.institutionauthor Özban, Ahmet Yaşar
dc.language.iso en en_US
dc.publisher Elsevier Science inc en_US
dc.relation.publicationcategory Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı en_US
dc.rights info:eu-repo/semantics/closedAccess en_US
dc.scopus.citedbyCount 3
dc.subject q-Integers en_US
dc.subject q-Bernstein polynomials en_US
dc.subject Convergence en_US
dc.subject Approximation of unbounded functions en_US
dc.subject Cauchy kernel en_US
dc.title The <i>q</I>-bernstein Polynomials of the Cauchy Kernel With a Pole on [0,1] in the Case <i>q</I> &gt; 1 en_US
dc.type Article en_US
dc.wos.citedbyCount 3
dspace.entity.type Publication
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