The new forms of Voronovskaya's theorem in weighted spaces

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dc.contributor.authorAcar, Tuncer
dc.contributor.authorAral, Ali
dc.contributor.authorRasa, Ioan
dc.date.accessioned2020-06-25T18:16:48Z
dc.date.available2020-06-25T18:16:48Z
dc.date.issued2016
dc.departmentKırıkkale Üniversitesi
dc.descriptionAcar, Tuncer/0000-0003-0982-9459; Rasa, Ioan/0000-0002-5206-030X
dc.description.abstractThe Voronovskaya theorem which is one of the most important pointwise convergence results in the theory of approximation by linear positive operators (l.p.o) is considered in quantitative form. Most of the results presented in this paper mainly depend on the Taylor's formula for the functions belonging to weighted spaces. We first obtain an estimate for the remainder of Taylor's formula and by this estimate we give the Voronovskaya theorem in quantitative form for a class of sequences of l.p.o. The Gruss type approximation theorem and the Gruss-Voronovskaya-type theorem in quantitative form are obtained as well. We also give the Voronovskaya type results for the difference of l.p.o acting on weighted spaces. All results are also given for well-known operators, Szasz-Mirakyan and Baskakov operators as illustrative examples. Our results being Voronovskaya-type either describe the rate of pointwise convergence or present the error of approximation simultaneously.en_US
dc.identifier.citationclosedAccessen_US
dc.identifier.doi10.1007/s11117-015-0338-4
dc.identifier.endpage40en_US
dc.identifier.issn1385-1292
dc.identifier.issn1572-9281
dc.identifier.issue1en_US
dc.identifier.scopus2-s2.0-84929094250
dc.identifier.scopusqualityQ2
dc.identifier.startpage25en_US
dc.identifier.urihttps://doi.org/10.1007/s11117-015-0338-4
dc.identifier.urihttps://hdl.handle.net/20.500.12587/6626
dc.identifier.volume20en_US
dc.identifier.wosWOS:000370794100002
dc.identifier.wosqualityQ2
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherSpringeren_US
dc.relation.ispartofPositivity
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectVoronovskaya theoremen_US
dc.subjectGruss-type-Voronovskaya theoremen_US
dc.subjectWeighted modulus of continuityen_US
dc.subjectDifference of operatorsen_US
dc.titleThe new forms of Voronovskaya's theorem in weighted spacesen_US
dc.typeArticle

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