General Tauberian theorems for the Cesaro integrability of functions
| dc.contributor.author | Totur, Umit | |
| dc.contributor.author | Canak, Ibrahim | |
| dc.date.accessioned | 2021-05-03T20:36:47Z | |
| dc.date.available | 2021-05-03T20:36:47Z | |
| dc.date.issued | 2020 | |
| dc.department | Ege Üniversitesi | en_US |
| dc.description.abstract | For a locally integrable function f on [0, infinity), we define F(t) = integral(t)(0) f(u) du and sigma(alpha)(t)= integral(t)(0) (1-u/t)(alpha) f(u) du for t > 0. The improper integral integral(infinity)(0) f(u) du is said to be (C, alpha) integrable to L for some alpha > -1 if the limit lim(x ->infinity) sigma(alpha)(t) = L exists. It is known that lim(x ->infinity) F(t) = l implies lim(x ->infinity) sigma(alpha)(t)= l for alpha > -1, but the converse of this implication is not true in general. in this paper, we introduce the concept of the general control modulo of non-integer order for functions and obtain some Tauberian conditions in terms of this concept for the (C, alpha) integrability method in order that the converse implication hold true. Our results extend the main theorems in [U. Totur and I. Canak, Tauberian conditions for the (C, alpha) integrability of functions, Positivity 21 (2017), no. 1, 73 83]. | en_US |
| dc.identifier.doi | 10.1515/gmj-2019-2005 | |
| dc.identifier.endpage | 527 | en_US |
| dc.identifier.issn | 1072-947X | |
| dc.identifier.issn | 1572-9176 | |
| dc.identifier.issue | 4 | en_US |
| dc.identifier.startpage | 517 | en_US |
| dc.identifier.uri | https://doi.org/10.1515/gmj-2019-2005 | |
| dc.identifier.uri | https://hdl.handle.net/11454/70218 | |
| dc.identifier.volume | 27 | en_US |
| dc.identifier.wos | WOS:000586530400003 | en_US |
| dc.identifier.wosquality | Q4 | en_US |
| dc.indekslendigikaynak | Web of Science | en_US |
| dc.language.iso | en | en_US |
| dc.publisher | Walter De Gruyter Gmbh | en_US |
| dc.relation.ispartof | Georgian Mathematical Journal | en_US |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| dc.rights | info:eu-repo/semantics/closedAccess | en_US |
| dc.subject | Cesaro integrability | en_US |
| dc.subject | (c, alpha) integrability | en_US |
| dc.subject | one-sided Tauberian condition | en_US |
| dc.subject | slow decreasing | en_US |
| dc.subject | Tauberian theorem and condition | en_US |
| dc.title | General Tauberian theorems for the Cesaro integrability of functions | en_US |
| dc.type | Article | en_US |
