{"title":"通过2赋范空间中序列的广义Nörlund均值的Tauberian定理","authors":"Valdete Loku","doi":"10.33039/ami.2022.07.001","DOIUrl":null,"url":null,"abstract":". In this paper, we will show Tauberian conditions under which ordinary convergence of the sequence ( 𝑥 𝑛 ) in 2-normed space 𝑋 , follows from 𝑇 𝑝,𝑞𝑛 -summability. In fact we give a necessary and sufficient Tauberian condition for this method of summability. Also, we prove that Tauberian Theorems for these summability methods are valid with Schmidt-type slowly oscillating condition as well as with Hardy-type “big O” condition.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":"391 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Tauberian theorems via the generalized Nörlund mean for sequences in 2-normed spaces\",\"authors\":\"Valdete Loku\",\"doi\":\"10.33039/ami.2022.07.001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". In this paper, we will show Tauberian conditions under which ordinary convergence of the sequence ( 𝑥 𝑛 ) in 2-normed space 𝑋 , follows from 𝑇 𝑝,𝑞𝑛 -summability. In fact we give a necessary and sufficient Tauberian condition for this method of summability. Also, we prove that Tauberian Theorems for these summability methods are valid with Schmidt-type slowly oscillating condition as well as with Hardy-type “big O” condition.\",\"PeriodicalId\":43454,\"journal\":{\"name\":\"Annales Mathematicae et Informaticae\",\"volume\":\"391 1\",\"pages\":\"\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales Mathematicae et Informaticae\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.33039/ami.2022.07.001\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Mathematicae et Informaticae","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33039/ami.2022.07.001","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Tauberian theorems via the generalized Nörlund mean for sequences in 2-normed spaces
. In this paper, we will show Tauberian conditions under which ordinary convergence of the sequence ( 𝑥 𝑛 ) in 2-normed space 𝑋 , follows from 𝑇 𝑝,𝑞𝑛 -summability. In fact we give a necessary and sufficient Tauberian condition for this method of summability. Also, we prove that Tauberian Theorems for these summability methods are valid with Schmidt-type slowly oscillating condition as well as with Hardy-type “big O” condition.
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