{"title":"渐赋范线性空间中序列的统计收敛性","authors":"C. Choudhury, S. Debnath","doi":"10.52846/ami.v49i1.1518","DOIUrl":null,"url":null,"abstract":"In this paper, we introduce and investigate the notion of lacunary statistical convergence of sequences in gradual normed linear spaces. We study some of its basic properties and some inclusion relations. In the end, we introduce the notion of lacunary statistical Cauchy sequences and prove that it is equivalent to the notion of lacunary statistical convergence.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":"16 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2022-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"On lacunary statistical convergence of sequences in gradual normed linear spaces\",\"authors\":\"C. Choudhury, S. Debnath\",\"doi\":\"10.52846/ami.v49i1.1518\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we introduce and investigate the notion of lacunary statistical convergence of sequences in gradual normed linear spaces. We study some of its basic properties and some inclusion relations. In the end, we introduce the notion of lacunary statistical Cauchy sequences and prove that it is equivalent to the notion of lacunary statistical convergence.\",\"PeriodicalId\":43654,\"journal\":{\"name\":\"Annals of the University of Craiova-Mathematics and Computer Science Series\",\"volume\":\"16 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2022-06-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of the University of Craiova-Mathematics and Computer Science Series\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.52846/ami.v49i1.1518\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of the University of Craiova-Mathematics and Computer Science Series","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.52846/ami.v49i1.1518","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
On lacunary statistical convergence of sequences in gradual normed linear spaces
In this paper, we introduce and investigate the notion of lacunary statistical convergence of sequences in gradual normed linear spaces. We study some of its basic properties and some inclusion relations. In the end, we introduce the notion of lacunary statistical Cauchy sequences and prove that it is equivalent to the notion of lacunary statistical convergence.