{"title":"ON f− STATİSTİCAL CONVERGENCE OF FRACTİONAL DİFFERENCE ON DOUBLE SEQUENCES","authors":"Koray İbrahim Atabey, Muhammed Çinar","doi":"10.22190/fumi211029044a","DOIUrl":null,"url":null,"abstract":"In this paper, using the fractional difference operator and a modulus function we introduce the concepts of $({}^{}_{2}{\\Delta_{\\beta}^{\\tilde{\\alpha}}},f)-$ statistical convergence, $({}^{}_{2}{\\Delta^{\\tilde{\\alpha}}},f)-$ statistical Cauchy and p-strongly $({}^{}_{2}{\\Delta^{\\tilde{\\alpha}}},f)-$ Cesàro summability, $(0<p<\\infty)$ for double sequences. We also give some inclusion relations between $({}^{}_{2}{\\Delta^{\\tilde{\\alpha}}},f)-$ statistical convergence and p-strongly $({}^{}_{2}{\\Delta^{\\tilde{\\alpha}}},f)-$ Cesàro summability $(0<p<\\infty)$.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"30 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2022-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Facta Universitatis-Series Mathematics and Informatics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22190/fumi211029044a","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: 0
Abstract
In this paper, using the fractional difference operator and a modulus function we introduce the concepts of $({}^{}_{2}{\Delta_{\beta}^{\tilde{\alpha}}},f)-$ statistical convergence, $({}^{}_{2}{\Delta^{\tilde{\alpha}}},f)-$ statistical Cauchy and p-strongly $({}^{}_{2}{\Delta^{\tilde{\alpha}}},f)-$ Cesàro summability, $(0