The Picard and Gauss-Weierstrass Singular Integrals in (p, q)-Calculus

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dc.contributor.authorAral, A.
dc.contributor.authorDeniz, E.
dc.contributor.authorErbay, H.
dc.date.accessioned2021-01-14T18:10:49Z
dc.date.available2021-01-14T18:10:49Z
dc.date.issued2020
dc.departmentKKÜ
dc.descriptionARAL, Ali/0000-0002-2024-8607; Erbay, Hasan/0000-0002-7555-541X
dc.description.abstractThe vast development of the techniques in both the quantum calculus and the post-quantum calculus leads to a significant increase in activities in approximation theory due to applications in computational science and engineering. Herein, we introduce (p, q)-Picard and (p, q)-Gauss-Weierstrass integral operators in terms of the (p, q)-Gamma integral. We give a general formula for the monomials under both (p, q)-Picard and (p, q)-Gauss-Weierstrass operators as well as some special cases. We discuss the uniform convergence properties of them. We show that both operators have optimal global smoothness preservation property via usual modulus of continuity. Finally, we establish the rate of approximation using the weighted modulus of smoothness. Depending on the choices of parameters p and q in the integrals, we are able to obtain better error estimation than classical ones.en_US
dc.identifier.citationBu makale açık erişimli değildir.en_US
dc.identifier.doi10.1007/s40840-019-00759-z
dc.identifier.endpage1583en_US
dc.identifier.issn0126-6705
dc.identifier.issn2180-4206
dc.identifier.issue2en_US
dc.identifier.scopus2-s2.0-85079152973
dc.identifier.scopusqualityQ1
dc.identifier.startpage1569en_US
dc.identifier.urihttps://doi.org/10.1007/s40840-019-00759-z
dc.identifier.urihttps://hdl.handle.net/20.500.12587/12785
dc.identifier.volume43en_US
dc.identifier.wosWOS:000526029300033
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherMALAYSIAN MATHEMATICAL SCIENCES SOCen_US
dc.relation.ispartofBULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subject(pen_US
dc.subjectq)-Picard integral operatoren_US
dc.subject(pen_US
dc.subjectq)-Gauss-Weierstrass integral operatoren_US
dc.subjectUniform convergenceen_US
dc.subjectGlobal smoothnessen_US
dc.titleThe Picard and Gauss-Weierstrass Singular Integrals in (p, q)-Calculusen_US
dc.typeArticle

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