The Approximation of Logarithmic Function by <i>q</I>-bernstein Polynomials in the Case <i>q</I> &gt; 1

dc.authorscopusid 35610828900
dc.authorwosid Ostrovska, Sofiya/AAA-2156-2020
dc.contributor.author Ostrovska, Sofiya
dc.contributor.other Mathematics
dc.date.accessioned 2024-07-05T14:33:28Z
dc.date.available 2024-07-05T14:33:28Z
dc.date.issued 2007
dc.department Atılım University en_US
dc.department-temp Atilim Univ, Dept Math, TR-06836 Ankara, Turkey en_US
dc.description.abstract Since 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) remains open. It is known that the approximation occurs for functions admitting an analytic continuation into a disc {z : | z| < R}, R > 1. For functions without such an assumption, no general results on approximation are available. In this paper, it is shown that the function f ( x) = ln( x + a), a > 0, is uniformly approximated by its q-Bernstein polynomials ( q > 1) on the interval [ 0, 1] if and only if a >= 1. en_US
dc.identifier.citationcount 9
dc.identifier.doi 10.1007/s11075-007-9081-7
dc.identifier.endpage 82 en_US
dc.identifier.issn 1017-1398
dc.identifier.issue 1 en_US
dc.identifier.scopus 2-s2.0-34248364864
dc.identifier.scopusquality Q1
dc.identifier.startpage 69 en_US
dc.identifier.uri https://doi.org/10.1007/s11075-007-9081-7
dc.identifier.uri https://hdl.handle.net/20.500.14411/936
dc.identifier.volume 44 en_US
dc.identifier.wos WOS:000246359200005
dc.identifier.wosquality Q1
dc.institutionauthor Ostrovska, Sofiya
dc.language.iso en en_US
dc.publisher Springer 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 9
dc.subject q-integers en_US
dc.subject q-binomial coefficients en_US
dc.subject q-Bernstein polynomials en_US
dc.subject uniform convergence en_US
dc.title The Approximation of Logarithmic Function by <i>q</I>-bernstein Polynomials in the Case <i>q</I> &gt; 1 en_US
dc.type Article en_US
dc.wos.citedbyCount 9
dspace.entity.type Publication
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relation.isOrgUnitOfPublication.latestForDiscovery 31ddeb89-24da-4427-917a-250e710b969c

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