<i>q</I>-bernstein Polynomials of the Cauchy Kernel

dc.authorscopusid 35610828900
dc.authorwosid Ostrovska, Sofiya/AAA-2156-2020
dc.contributor.author Ostrovska, Sofiya
dc.contributor.other Mathematics
dc.date.accessioned 2024-07-05T14:34:05Z
dc.date.available 2024-07-05T14:34:05Z
dc.date.issued 2008
dc.department Atılım University en_US
dc.department-temp Atilim Univ, Dept Math, TR-06836 Ankara, Turkey en_US
dc.description.abstract Due to the fact that in the case q > 1, q-Bernstein polynomials are not positive linear operators on C[0, 1], the study of their approximation properties is essentially more difficult than that for 0 < q < 1. Despite the intensive research conducted in the area lately, the problem of describing the class of functions in C[0, 1] uniformly approximated by their q-Bernstein polynomials (q > 1) is still open. In this paper, the q-Bernstein polynomials B-n,B-q(f(a); z) of the Cauchy kernel f(a) = 1/(z - a), a is an element of C \ [0, 1] are found explicitly and their properties are investigated. In particular, it is proved that if q > 1, then polynomials B-n,B-q(f(a); z) converge to f(a) uniformly on any compact set K subset of {z : vertical bar z vertical bar < vertical bar a vertical bar}. This result is sharp in the following sense: on any set with an accumulation point in {z : vertical bar z vertical bar > vertical bar a vertical bar}, the sequence {B-n,B-q(f(a); z) is not even uniformly bounded. (C) 2007 Elsevier Inc. All rights reserved. en_US
dc.identifier.citationcount 16
dc.identifier.doi 10.1016/j.amc.2007.08.066
dc.identifier.endpage 270 en_US
dc.identifier.issn 0096-3003
dc.identifier.issn 1873-5649
dc.identifier.issue 1 en_US
dc.identifier.scopus 2-s2.0-40149083412
dc.identifier.startpage 261 en_US
dc.identifier.uri https://doi.org/10.1016/j.amc.2007.08.066
dc.identifier.uri https://hdl.handle.net/20.500.14411/1018
dc.identifier.volume 198 en_US
dc.identifier.wos WOS:000254254300022
dc.identifier.wosquality Q1
dc.institutionauthor Ostrovska, Sofiya
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 16
dc.subject q-Bernstein polynomials en_US
dc.subject Cauchy kernel en_US
dc.subject analytic function en_US
dc.subject convergence en_US
dc.title <i>q</I>-bernstein Polynomials of the Cauchy Kernel en_US
dc.type Article en_US
dc.wos.citedbyCount 16
dspace.entity.type Publication
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relation.isOrgUnitOfPublication.latestForDiscovery 31ddeb89-24da-4427-917a-250e710b969c

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