The Norm Estimates of the <i>q</I>-bernstein Operators for Varying <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 2024-07-05T15:10:12Z
dc.date.available 2024-07-05T15:10:12Z
dc.date.issued 2011
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 aim of this paper is to present norm estimates in C [0, 1] for the q-Bernstein basic polynomials and the q-Bernstein operators B-n,B-q in the case q > 1. While for 0 < q <= 1, vertical bar vertical bar B-n,B-q vertical bar vertical bar = 1 for all n is an element of N. in the case q > 1, the norm vertical bar vertical bar B-n,B-q vertical bar vertical bar increases rather rapidly as q -> +infinity. In this study, it is proved that vertical bar vertical bar B-n,B-q vertical bar vertical bar similar to C(n)q(n(n-1)/2), q -> +infinity with C-n = 2/n (1- 1/n)(n-1). Moreover, it is shown that vertical bar vertical bar B-n,B-q vertical bar vertical bar similar to 2q(n(n-1)/2) /ne as n -> infinity, q -> +infinity. The results of the paper are illustrated by numerical examples. (C) 2011 Elsevier Ltd. All rights reserved. en_US
dc.identifier.citationcount 6
dc.identifier.doi 10.1016/j.camwa.2011.10.067
dc.identifier.endpage 4771 en_US
dc.identifier.issn 0898-1221
dc.identifier.issn 1873-7668
dc.identifier.issue 12 en_US
dc.identifier.scopus 2-s2.0-82255160739
dc.identifier.startpage 4758 en_US
dc.identifier.uri https://doi.org/10.1016/j.camwa.2011.10.067
dc.identifier.uri https://hdl.handle.net/20.500.14411/1284
dc.identifier.volume 62 en_US
dc.identifier.wos WOS:000298824900047
dc.identifier.wosquality Q1
dc.institutionauthor Ostrovska, Sofiya
dc.institutionauthor Özban, Ahmet Yaşar
dc.language.iso en en_US
dc.publisher Pergamon-elsevier Science Ltd 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 6
dc.subject q-integers en_US
dc.subject q-binomial coefficients en_US
dc.subject q-Bernstein polynomials en_US
dc.subject q-Bernstein operator en_US
dc.subject Operator norm en_US
dc.subject Newton's method en_US
dc.title The Norm Estimates of the <i>q</I>-bernstein Operators for Varying <i>q</I> &gt; 1 en_US
dc.type Article en_US
dc.wos.citedbyCount 5
dspace.entity.type Publication
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