Tauberian theorems for the product of weighted and cesaro summability methods of double sequences
| dc.authorid | 0000-0002-2356-3987 | en_US |
| dc.authorid | 0000-0002-1754-1685 | en_US |
| dc.contributor.author | Fındık, Gökşen | |
| dc.contributor.author | Çanak, İbrahim | |
| dc.date.accessioned | 2024-07-12T20:46:45Z | |
| dc.date.available | 2024-07-12T20:46:45Z | |
| dc.date.issued | 2019 | en_US |
| dc.department | Fakülteler, İnsan ve Toplum Bilimleri Fakültesi, Matematik Bölümü | en_US |
| dc.description.abstract | A double sequence u = (umn) is called convergent in Pringsheim’s sense (in short P-convergent) to s [? ], if for a given ? > 0 there exists a positive integer N0 such that |umn ? s| < ? for all nonnegative integers m, n ? N0. (C, 1, 1) means of (umn) are defined by ? (11) mn (u) := 1 (m + 1)(n + 1) ?m i=0 ?n j=0 ui j for all nonnegative integers m and n. Similarly, (C, 1, 0) and (C, 0, 1) means of (umn) are defined respectively by ? (10) mn (u) := 1 m + 1 ?m i=0 uin, ?(01) mn (u) := 1 n + 1 ?n j=0 um j for all nonnegative integers m and n. A sequence (umn) is said to be (C, ?, ?) summable to s if lim m,n?? ? (??) mn (u) = s, where (?, ?) = (1, 1), (1, 0) and (0, 1). In this case, we write umn ? s (C, ?, ?). Let p := {pk} ? k=0 and q := {ql} ? l=0 be sequences of nonnegative real numbers with p0, q0 > 0 such that Pm := ?m k=0 pk , 0 for all m ? 0 and Qn := ?n l=0 ql , 0 for all n ? 0. The weighted means t (??) mn of a double sequence (umn), in short, the ( N, p, q; ?, ?) means, are defined respectively by tmn(u) = t (11) mn (u) := 1 PmQn ?m k=0 ?n l=0 pkqlukl, t (10) mn (u) = 1 Pm ?m k=0 pkukn, t (01) mn (u) = 1 Qn ?n l=0 qluml where m, n ? 0. A sequence (umn) is said to be summable by the weighted mean method determined by the sequences p and q, in short, summable (N, p, q; ?, ?) where (?, ?) = (1, 1), (1, 0), (0, 1) if lim m,n?? t (??) mn = s. In this case, we write umn ? s ( N, p, q; ?, ?) . The product of ( N, p, q; 1, 1 ) and (C, ?, ?) summability is defined by ( N, p, q; 1, 1 ) (C, ?, ?) summability, where (?, ?) = (1, 1), (1, 0), (0, 1). | en_US |
| dc.identifier.citation | Fındık, G., Çanak, İ. (2019). Tauberian theorems for the product of weighted and cesaro summability methods of double sequences. International Conference of Mathematical Sciences. 030018(1)-030018(4). | en_US |
| dc.identifier.endpage | 030018-4 | en_US |
| dc.identifier.isbn | 978-0-7354-1816-5 | |
| dc.identifier.startpage | 030018-1 | en_US |
| dc.identifier.uri | https://aip.scitation.org/doi/10.1063/1.5095103 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12415/1903 | |
| dc.language.iso | en | en_US |
| dc.publisher | Maltepe Üniversitesi | en_US |
| dc.relation.ispartof | International Conference of Mathematical Sciences | en_US |
| dc.relation.isversionof | 10.1063/1.5095103 | en_US |
| dc.relation.publicationcategory | Uluslararası Konferans Öğesi - Başka Kurum Yazarı | en_US |
| dc.rights | CC0 1.0 Universal | * |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.rights.uri | http://creativecommons.org/publicdomain/zero/1.0/ | * |
| dc.snmz | KY01362 | |
| dc.subject | Tauberian theorems | en_US |
| dc.subject | Double sequences | en_US |
| dc.subject | Cesaro means | en_US |
| dc.subject | Weighted means | en_US |
| dc.subject | Convergence in Pringsheim’s sense | en_US |
| dc.subject | Weighted- ` Cesaro summability | en_US |
| dc.title | Tauberian theorems for the product of weighted and cesaro summability methods of double sequences | en_US |
| dc.type | Article | |
| dspace.entity.type | Publication |
