{"title":"ON I- CONVERGENCE OF SEQUENCES IN GRADUAL NORMED LINEAR SPACES","authors":"C. Choudhury, S. Debnath","doi":"10.22190/fumi210108044c","DOIUrl":null,"url":null,"abstract":"In this paper, we introduce the concepts of $\\mathcal{I}$ and $\\mathcal{I^{*}}-$convergence of sequences in gradual normed linear spaces. We study some basic properties and implication relations of the newly defined convergence concepts. Also, we introduce the notions of $\\mathcal{I}$ and $\\mathcal{I^{*}}-$Cauchy sequences in the gradual normed linear space and investigate the relations between them.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"23 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2021-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Facta Universitatis-Series Mathematics and Informatics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22190/fumi210108044c","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 3
Abstract
In this paper, we introduce the concepts of $\mathcal{I}$ and $\mathcal{I^{*}}-$convergence of sequences in gradual normed linear spaces. We study some basic properties and implication relations of the newly defined convergence concepts. Also, we introduce the notions of $\mathcal{I}$ and $\mathcal{I^{*}}-$Cauchy sequences in the gradual normed linear space and investigate the relations between them.