Tauberian Conditions Under which Convergence Follows from the Weighted Mean Summability and Its Statistical Extension for Sequences of Fuzzy Numbers

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dc.authorscopusid56523030200
dc.authorscopusid10140301300
dc.contributor.authorOnder, Z.
dc.contributor.authorCanak, I
dc.date.accessioned2023-01-12T19:50:52Z
dc.date.available2023-01-12T19:50:52Z
dc.date.issued2022
dc.departmentN/A/Departmenten_US
dc.description.abstractLet (p(n)) be a sequence of nonnegative numbers such that p(0) > 0 and P-n:= Sigma(n)(k=0)p(k)->infinity as n -> infinity. Let (u(n)) be a sequence of fuzzy numbers. The weighted mean of (u(n)) is defined by t(n) := 1/P-n Sigma(n)(k=0)pkuk for n = 0,1,1,2,... It is known that the existence of the limit lim u(n) = mu(0) implies that lim t(n) = mu(0). For the existence of the limit st-lim t(n) = mu(0), we require the boundedness of (u(n)) in addition to the existence of the limit lim u(n) = mu(0). However, in general, the converse of this implication is not true. We establish Tauberian conditions, under which the existence of the limit lim u(n) = mu(0) follows from the existence of the limit lim t(n) = mu(0) or st-lim t(n) = mu(0). These Tauberian conditions are satisfied if (u(n)) satisfies the two-sided condition of Hardy type relative to (P-n).en_US
dc.identifier.doi10.1007/s11253-022-01989-4
dc.identifier.endpage1277en_US
dc.identifier.issn0041-5995
dc.identifier.issn1573-9376
dc.identifier.issn0041-5995en_US
dc.identifier.issn1573-9376en_US
dc.identifier.issue8en_US
dc.identifier.scopus2-s2.0-85124101958en_US
dc.identifier.scopusqualityQ3en_US
dc.identifier.startpage1259en_US
dc.identifier.urihttps://doi.org/10.1007/s11253-022-01989-4
dc.identifier.urihttps://hdl.handle.net/11454/76185
dc.identifier.volume73en_US
dc.identifier.wosWOS:000749930100003en_US
dc.identifier.wosqualityQ4en_US
dc.indekslendigikaynakScopusen_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.language.isoenen_US
dc.publisherSpringeren_US
dc.relation.ispartofUkrainian Mathematical Journalen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectAlphaen_US
dc.titleTauberian Conditions Under which Convergence Follows from the Weighted Mean Summability and Its Statistical Extension for Sequences of Fuzzy Numbersen_US
dc.typeArticleen_US

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