Rough statistical convergence on triple sequence of the Bernstein operator of random variables in probability

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dc.authorscopusid36816540800
dc.authorscopusid55927576700
dc.authorscopusid15754098100
dc.contributor.authorSubramanian N.
dc.contributor.authorEsi A.
dc.contributor.authorOzdemir M.K.
dc.date.accessioned2024-08-04T19:59:15Z
dc.date.available2024-08-04T19:59:15Z
dc.date.issued2019
dc.departmentİnönü Üniversitesien_US
dc.description.abstractThis paper aims to improve further on the work of Phu (2001), Aytar (2008), and Ghosal (2013). We propose a new apporach to extend the application area of rough statistical convergence usually used in triple sequence of the Bernstein operator of real numbers to the theory of probability distributions. The introduction of this concept in the probability of Bernstein polynomials of rough statistical convergence, Bernstein polynomials of rough strong Cesàro summable, Bernstein polynomials of rough lacunary statistical convergence, Bernstein polynomials of rough N? convergence, Bernstein polynomials of rough statistical convergence, and Bernstein polynomials of rough strong (V, ?)summable to generalize the convergence analysis to accommodate any form of distribution of random variables. Among these six concepts in probability only three convergences are distinct Bernstein polynomials of rough statistical convergence: (1) Bernstein polynomials of rough lacunary statistical convergence, (2) Bernstein polynomials of rough statistical convergence where Bernstein polynomials of rough strong Cesàro summable is equivalent to Bernstein polynomials of rough statistical convergence, and (3) Bernstein polynomials of rough N?-convergence which is equivalent to Bernstein polynomials of rough lacunary statistical convergence. Bernstein polynomials of rough strong (V, ?)-summable is equivalent to Bernstein polynomials of rough ? statistical convergence. Basic properties and interrelations of these three distinct convergences are investigated and some observations were made in these classes and in this way we demonstrated that rough statistical convergence in probability is the more generalized concept than the usual Bernstein polynomials of rough statistical convergence. © 2019, Prince of Songkla University. All rights reserved.en_US
dc.identifier.doi10.14456/sjst-psu.2019.87
dc.identifier.endpage579en_US
dc.identifier.issn0125-3395
dc.identifier.issue3en_US
dc.identifier.scopus2-s2.0-85071341481en_US
dc.identifier.scopusqualityQ3en_US
dc.identifier.startpage567en_US
dc.identifier.urihttps://doi.org/10.14456/sjst-psu.2019.87
dc.identifier.urihttps://hdl.handle.net/11616/90503
dc.identifier.volume41en_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherPrince of Songkla Universityen_US
dc.relation.ispartofSongklanakarin Journal of Science and Technologyen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectBernstein polynomialsen_US
dc.subjectRough lacunary statistical convergenceen_US
dc.subjectRough n?-convergenceen_US
dc.subjectRough statistical convergenceen_US
dc.subjectRough strong (v,?)- summableen_US
dc.subjectRough strong cesàro summableen_US
dc.subjectRough ?- statistical convergenceen_US
dc.titleRough statistical convergence on triple sequence of the Bernstein operator of random variables in probabilityen_US
dc.typeArticleen_US

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