{"title":"Lacunary Statistical Equivalence of Order \\(\\eta\\) for Double Sequences of Sets","authors":"Uğur Ulusu","doi":"10.1007/s40010-023-00818-y","DOIUrl":null,"url":null,"abstract":"<div><p>In this study, by introducing the concepts of asymptotical lacunary statistical and asymptotical strong <i>p</i>-lacunary equivalence of order <span>\\(\\eta \\)</span> (<span>\\(0<\\eta \\le 1\\)</span>) in the Wijsman sense for double set sequences, some properties of these concepts are examined and also the relationship between these concepts is mentioned. Moreover, the relationships between these concepts and the asymptotical equivalence concepts previously given for double set sequences are investigated.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","FirstCategoryId":"103","ListUrlMain":"https://link.springer.com/article/10.1007/s40010-023-00818-y","RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
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Abstract
In this study, by introducing the concepts of asymptotical lacunary statistical and asymptotical strong p-lacunary equivalence of order \(\eta \) (\(0<\eta \le 1\)) in the Wijsman sense for double set sequences, some properties of these concepts are examined and also the relationship between these concepts is mentioned. Moreover, the relationships between these concepts and the asymptotical equivalence concepts previously given for double set sequences are investigated.
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