{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:30:01Z","timestamp":1753882201792,"version":"3.41.2"},"reference-count":10,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,11,16]],"date-time":"2006-11-16T00:00:00Z","timestamp":1163635200000},"content-version":"vor","delay-in-days":319,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100002679","name":"Adnan Menderes University","doi-asserted-by":"crossref","award":["FEF-06011"],"award-info":[{"award-number":["FEF-06011"]}],"id":[{"id":"10.13039\/501100002679","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>Let (<jats:italic>u<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>)\n be a sequence of real numbers, <jats:italic>L<\/jats:italic>\n an additive\nlimitable method with some property, and  and\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t different spaces of sequences related to each other.\nWe prove that if the classical control modulo of the oscillatory\nbehavior of (<jats:italic>u<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>) in   is a Tauberian condition\nfor <jats:italic>L<\/jats:italic>, then the general control modulo of the oscillatory\nbehavior of integer order <jats:italic>m<\/jats:italic> of (<jats:italic>u<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>)\n in  or\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t is also a Tauberian condition for <jats:italic>L<\/jats:italic>.<\/jats:p>","DOI":"10.1155\/ijmms\/2006\/82342","type":"journal-article","created":{"date-parts":[[2006,12,4]],"date-time":"2006-12-04T07:12:10Z","timestamp":1165216330000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Tauberian conditions for a general limitable method"],"prefix":"10.1155","volume":"2006","author":[{"given":"\u0130brahim","family":"Canak","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"\u00dcmit","family":"Totur","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,16]]},"reference":[{"key":"e_1_2_1_1_2","doi-asserted-by":"publisher","DOI":"10.1155\/IJMMS.2005.2491"},{"key":"e_1_2_1_2_2","unstructured":"Danak\u0130.andTotur\u00dc. A Tauberian theorem with a generalized one-sided condition preprint 2005."},{"key":"e_1_2_1_3_2","unstructured":"Danak\u0130.andTotur\u00dc. Tauberian theorems for Abel limitable sequences with controlled oscillatory behavior preprint 2006."},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.5937\/MatMor0105057D"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s2-13.1.174"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s2-9.1.434"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1967-11851-2"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01479600"},{"key":"e_1_2_1_9_2","series-title":"edited by I. Danak, Graduate Research Seminar Lecture Notes","volume-title":"Analysis of Divergence: Control and Management of Divergent Processes","author":"Stanojevi\u0107 \u010c. V.","year":"1998"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01696278"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2006\/082342.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/IJMMS\/2006\/82342","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,6]],"date-time":"2024-06-06T21:15:41Z","timestamp":1717708541000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/IJMMS\/2006\/82342"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,1]]},"references-count":10,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2006,1]]}},"alternative-id":["10.1155\/IJMMS\/2006\/82342"],"URL":"https:\/\/doi.org\/10.1155\/ijmms\/2006\/82342","archive":["Portico"],"relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2006,1]]},"assertion":[{"value":"2006-11-16","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"082342"}}