On the Convergence of the <i>q</I>-bernstein Polynomials for Power Functions

dc.authorid Ostrovska, Sofiya/0000-0003-1842-7953
dc.authorscopusid 35610828900
dc.authorscopusid 9276702800
dc.contributor.author Ostrovska, Sofiya
dc.contributor.author Ozban, Ahmet Yasar
dc.contributor.other Mathematics
dc.date.accessioned 2024-07-05T15:21:27Z
dc.date.available 2024-07-05T15:21:27Z
dc.date.issued 2021
dc.department Atılım University en_US
dc.department-temp [Ostrovska, Sofiya] Atilim Univ, Dept Math, TR-06836 Ankara, Turkey; [Ozban, Ahmet Yasar] Cankiri Karatekin Univ, Dept Math, TR-18100 Cankiri, Turkey; [Ozban, Ahmet Yasar] OSYM Baskanligi, TR-06800 Ankara, Turkey en_US
dc.description Ostrovska, Sofiya/0000-0003-1842-7953 en_US
dc.description.abstract The aim of this paper is to present new results related to the convergence of the sequence of the complex q-Bernstein polynomials {B-n,B-q(f(alpha); z)}, where 0 < q not equal 1 and f(alpha) = x(alpha), alpha >= 0, is a power function on [0, 1]. This study makes it possible to describe all feasible sets of convergence K for such polynomials. Specifically, if either 0 < q < 1 or alpha is an element of N-0, then K = C, otherwise K = {0} boolean OR {q(-j)}(j=0)(infinity). In the latter case, this identifies the sequence K = {0} boolean OR {q(-j)}(j=0)(infinity) as the 'minimal' set of convergence for polynomials B-n,B-q(f; z), f is an element of C[0, 1] in the case q > 1. In addition, the asymptotic behavior of the polynomials {B-n,B-q(f(alpha); z)}, with q > 1 has been investigated and the obtained results are illustrated by numerical examples. en_US
dc.identifier.citationcount 0
dc.identifier.doi 10.1007/s00009-021-01756-y
dc.identifier.issn 1660-5446
dc.identifier.issn 1660-5454
dc.identifier.issue 3 en_US
dc.identifier.scopus 2-s2.0-85104256182
dc.identifier.scopusquality Q2
dc.identifier.uri https://doi.org/10.1007/s00009-021-01756-y
dc.identifier.uri https://hdl.handle.net/20.500.14411/2087
dc.identifier.volume 18 en_US
dc.identifier.wos WOS:000639444200001
dc.identifier.wosquality Q2
dc.institutionauthor Ostrovska, Sofiya
dc.institutionauthor Özban, Ahmet Yaşar
dc.language.iso en en_US
dc.publisher Springer Basel Ag 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 0
dc.subject q-integer en_US
dc.subject q-Bernstein polynomial en_US
dc.subject Power function en_US
dc.subject Convergence en_US
dc.title On the Convergence of the <i>q</I>-bernstein Polynomials for Power Functions en_US
dc.type Article en_US
dc.wos.citedbyCount 0
dspace.entity.type Publication
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relation.isOrgUnitOfPublication.latestForDiscovery 31ddeb89-24da-4427-917a-250e710b969c

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